diff --git a/src/Bridges/Variable/map.jl b/src/Bridges/Variable/map.jl
index cfe16733b3..eca4290a41 100644
--- a/src/Bridges/Variable/map.jl
+++ b/src/Bridges/Variable/map.jl
@@ -579,11 +579,13 @@ Throw an error if some bridged variables do not have any reverse mapping.
 """
 function throw_if_cannot_unbridge(map::Map)
     if map.unbridged_function === nothing
-        error(
-            "Cannot unbridge function because some variables are bridged by",
-            " variable bridges that do not support reverse mapping, for example,",
-            " `ZerosBridge`.",
+        err = MOI.GetAttributeNotAllowed(
+            MOI.ConstraintFunction(),
+            "Cannot unbridge function because some variables are bridged by " *
+            "variable bridges that do not support reverse mapping, for " *
+            "example, `ZerosBridge`.",
         )
+        throw(err)
     end
 end
 
diff --git a/test/Bridges/Variable/map.jl b/test/Bridges/Variable/map.jl
index d519273ad0..932b01d912 100644
--- a/test/Bridges/Variable/map.jl
+++ b/test/Bridges/Variable/map.jl
@@ -54,7 +54,8 @@ function test_map()
     S1 = typeof(set1)
     v1, c1 = MOI.Bridges.Variable.add_key_for_bridge(map, () -> b1, set1)
     MOI.is_valid(map, c1)
-    cannot_unbridge_err = ErrorException(
+    cannot_unbridge_err = MOI.GetAttributeNotAllowed(
+        MOI.ConstraintFunction(),
         "Cannot unbridge function because some variables are bridged by variable" *
         " bridges that do not support reverse mapping, for example, `ZerosBridge`.",
     )
diff --git a/test/Bridges/Variable/zeros.jl b/test/Bridges/Variable/zeros.jl
index 73cf9d779a..923bc868b0 100644
--- a/test/Bridges/Variable/zeros.jl
+++ b/test/Bridges/Variable/zeros.jl
@@ -84,14 +84,15 @@ function test_zeros()
     )
     @test_throws err MOI.delete(bridged_mock, cyz)
 
-    err = ErrorException(
+    err = MOI.GetAttributeNotAllowed(
+        MOI.ConstraintFunction(),
         "Cannot unbridge function because some variables are bridged by" *
         " variable bridges that do not support reverse mapping, for example," *
         " `ZerosBridge`.",
     )
     @test_throws err MOI.get(bridged_mock, MOI.ObjectiveFunction{typeof(obj)}())
     # With `c1`, the function does not contain any variable so it tests that it
-    # also throws an error even if it never calls `variable_unbridged_function`.
+    # also throws an error even if it never calls `variable_unbridged_function`
     @test_throws err MOI.get(bridged_mock, MOI.ConstraintFunction(), c1)
     @test_throws err MOI.get(bridged_mock, MOI.ConstraintFunction(), c2)
 
diff --git a/test/Bridges/bridge_optimizer.jl b/test/Bridges/bridge_optimizer.jl
index 9493f4c0e4..97fe163f03 100644
--- a/test/Bridges/bridge_optimizer.jl
+++ b/test/Bridges/bridge_optimizer.jl
@@ -1176,6 +1176,17 @@ function test_ListOfVariablesWithAttributeSet(T = Float64)
     return
 end
 
+function test_cannot_unbridge_variable_function()
+    model = MOI.Bridges.Variable.Zeros{Float64}(MOI.Utilities.Model{Float64}())
+    x, c = MOI.add_constrained_variables(model, MOI.Zeros(1))
+    c2 = MOI.add_constraint(model, 1.0 * x[1], MOI.EqualTo(1.0))
+    @test_throws(
+        MOI.GetAttributeNotAllowed{MOI.ConstraintFunction},
+        MOI.get(model, MOI.ConstraintFunction(), c2),
+    )
+    return
+end
+
 end  # module
 
 TestBridgeOptimizer.runtests()