diff --git a/src/com/google/javascript/jscomp/BranchCoverageInstrumentationCallback.java b/src/com/google/javascript/jscomp/BranchCoverageInstrumentationCallback.java
index 1b3828b8003..16433babb03 100644
--- a/src/com/google/javascript/jscomp/BranchCoverageInstrumentationCallback.java
+++ b/src/com/google/javascript/jscomp/BranchCoverageInstrumentationCallback.java
@@ -51,8 +51,10 @@ public void visit(NodeTraversal traversal, Node node, Node parent) {
 
     if (node.isScript()) {
       if (instrumentationData.get(fileName) != null) {
+        Node toAddTo =
+            node.hasChildren() && node.getFirstChild().isModuleBody() ? node.getFirstChild() : node;
         // Add instrumentation code
-        node.addChildrenToFront(newHeaderNode(traversal, node).removeChildren());
+        toAddTo.addChildrenToFront(newHeaderNode(traversal, toAddTo).removeChildren());
         compiler.reportChangeToEnclosingScope(node);
         instrumentBranchCoverage(traversal, instrumentationData.get(fileName));
       }
diff --git a/src/com/google/javascript/jscomp/CoverageInstrumentationCallback.java b/src/com/google/javascript/jscomp/CoverageInstrumentationCallback.java
index 437141c7f7b..df4f79d3b01 100644
--- a/src/com/google/javascript/jscomp/CoverageInstrumentationCallback.java
+++ b/src/com/google/javascript/jscomp/CoverageInstrumentationCallback.java
@@ -150,6 +150,9 @@ public void visit(NodeTraversal traversal, Node node, Node parent) {
     if (node.isScript()) {
       String fileName = getFileName(traversal);
       if (instrumentationData.get(fileName) != null) {
+        if (node.hasChildren() && node.getFirstChild().isModuleBody()) {
+          node = node.getFirstChild();
+        }
         node.addChildrenToFront(newHeaderNode(traversal, node).removeChildren());
       }
       traversal.reportCodeChange();
@@ -195,7 +198,7 @@ public void visit(NodeTraversal traversal, Node node, Node parent) {
     }
 
     // For any other statement, add instrumentation code just before it.
-    if (parent != null && NodeUtil.isStatementBlock(parent)) {
+    if (parent != null && NodeUtil.isStatementBlock(parent) && !node.isModuleBody()) {
       parent.addChildBefore(
           newInstrumentationNode(traversal, node),
           node);
diff --git a/src/com/google/javascript/jscomp/CoverageInstrumentationPass.java b/src/com/google/javascript/jscomp/CoverageInstrumentationPass.java
index 592e6564403..8994de0fc09 100644
--- a/src/com/google/javascript/jscomp/CoverageInstrumentationPass.java
+++ b/src/com/google/javascript/jscomp/CoverageInstrumentationPass.java
@@ -95,6 +95,11 @@ public void process(Node externsNode, Node rootNode) {
       }
       Node firstScript = rootNode.getFirstChild();
       checkState(firstScript.isScript());
+      // If any passes run after we need to preserve the MODULE_BODY structure of scripts - we can't
+      // just add to a script if it is a module.
+      if (firstScript.hasChildren() && firstScript.getFirstChild().isModuleBody()) {
+        firstScript = firstScript.getFirstChild();
+      }
       addHeaderCode(firstScript);
     }
   }
diff --git a/test/com/google/javascript/jscomp/CoverageInstrumentationPassTest.java b/test/com/google/javascript/jscomp/CoverageInstrumentationPassTest.java
index ca542db802f..d4ad55a482b 100644
--- a/test/com/google/javascript/jscomp/CoverageInstrumentationPassTest.java
+++ b/test/com/google/javascript/jscomp/CoverageInstrumentationPassTest.java
@@ -25,14 +25,19 @@
 @RunWith(JUnit4.class)
 public final class CoverageInstrumentationPassTest {
 
-  private CompilerOptions options(LanguageMode inMode) {
+  private CompilerOptions options(LanguageMode inMode, LanguageMode outMode, boolean coverageOnly) {
     CompilerOptions options = GoldenFileComparer.options();
     options.setInstrumentForCoverage(true);
+    options.setInstrumentForCoverageOnly(coverageOnly);
     options.setLanguageIn(inMode);
-    options.setLanguageOut(LanguageMode.ECMASCRIPT5);
+    options.setLanguageOut(outMode);
     return options;
   }
 
+  private CompilerOptions options(LanguageMode inMode) {
+    return options(inMode, LanguageMode.ECMASCRIPT5, /* coverageOnly= */ false);
+  }
+
   private CompilerOptions branchOptions(LanguageMode inMode) {
     CompilerOptions options = GoldenFileComparer.options();
     options.setInstrumentForCoverage(true);
@@ -152,4 +157,12 @@ public void testWhileLoopBranch() throws Exception {
     compareWhileLoopBranch(LanguageMode.ECMASCRIPT_2015);
   }
 
+  @Test
+  public void testEsModule() throws Exception {
+    GoldenFileComparer.compileAndCompare(
+        "CoverageInstrumentationPassTest/EsModuleGolden.jsdata",
+        options(
+            LanguageMode.ECMASCRIPT_NEXT, LanguageMode.ECMASCRIPT_NEXT, /* coverageOnly= */ true),
+        "CoverageInstrumentationPassTest/EsModule.jsdata");
+  }
 }
diff --git a/test/com/google/javascript/jscomp/testdata/CoverageInstrumentationPassTest/EsModule.jsdata b/test/com/google/javascript/jscomp/testdata/CoverageInstrumentationPassTest/EsModule.jsdata
new file mode 100644
index 00000000000..f8c70d09007
--- /dev/null
+++ b/test/com/google/javascript/jscomp/testdata/CoverageInstrumentationPassTest/EsModule.jsdata
@@ -0,0 +1,5 @@
+import * as foo from 'bar';
+
+export function qux() {
+  console.log('baz');
+}
\ No newline at end of file
diff --git a/test/com/google/javascript/jscomp/testdata/CoverageInstrumentationPassTest/EsModuleGolden.jsdata b/test/com/google/javascript/jscomp/testdata/CoverageInstrumentationPassTest/EsModuleGolden.jsdata
new file mode 100644
index 00000000000..65d1358a0cc
--- /dev/null
+++ b/test/com/google/javascript/jscomp/testdata/CoverageInstrumentationPassTest/EsModuleGolden.jsdata
@@ -0,0 +1,19 @@
+'use strict';
+if (!self.window) {
+  self.window = self;
+  self.window.top = self;
+}
+var __jscov = window.top["__jscov"] || (window.top["__jscov"] = {"fileNames":[], "instrumentedLines":[], "executedLines":[]});
+var JSCompiler_lcov_data_CoverageInstrumentationPassTest_EsModule_jsdata = [];
+__jscov["executedLines"].push(JSCompiler_lcov_data_CoverageInstrumentationPassTest_EsModule_jsdata);
+__jscov["instrumentedLines"].push("0d");
+__jscov["fileNames"].push("CoverageInstrumentationPassTest/EsModule.jsdata");
+JSCompiler_lcov_data_CoverageInstrumentationPassTest_EsModule_jsdata[0] = true;
+import*as foo from "bar";
+JSCompiler_lcov_data_CoverageInstrumentationPassTest_EsModule_jsdata[2] = true;
+export function qux() {
+  JSCompiler_lcov_data_CoverageInstrumentationPassTest_EsModule_jsdata[2] = true;
+  JSCompiler_lcov_data_CoverageInstrumentationPassTest_EsModule_jsdata[3] = true;
+  console.log("baz");
+}
+;
\ No newline at end of file