diff --git a/integration_test/myxql/storage_test.exs b/integration_test/myxql/storage_test.exs
index 62315a55f..df9b5c45b 100644
--- a/integration_test/myxql/storage_test.exs
+++ b/integration_test/myxql/storage_test.exs
@@ -26,8 +26,11 @@ defmodule Ecto.Integration.StorageTest do
     run_mysql("DROP DATABASE #{params()[:database]};")
   end
 
-  def create_database do
+  def create_database(grant_privileges_to \\ nil) do
     run_mysql("CREATE DATABASE #{params()[:database]};")
+    if grant_privileges_to do
+      run_mysql("GRANT ALL PRIVILEGES ON #{params()[:database]}.* to #{grant_privileges_to}")
+    end
   end
 
   def create_posts do
@@ -73,6 +76,20 @@ defmodule Ecto.Integration.StorageTest do
     drop_database()
   end
 
+  test "storage up with unprivileged user with access to the database" do
+    unprivileged_params = Keyword.merge(params(),
+      username: "unprivileged",
+      password: "pass"
+    )
+    run_mysql("CREATE USER unprivileged IDENTIFIED BY 'pass'")
+    refute Ecto.Adapters.MyXQL.storage_up(unprivileged_params) == :ok
+    create_database("unprivileged")
+    assert Ecto.Adapters.MyXQL.storage_up(unprivileged_params) == {:error, :already_up}
+  after
+    run_mysql("DROP USER unprivileged")
+    drop_database()
+  end
+
   test "structure dump and load" do
     create_database()
     create_posts()
diff --git a/integration_test/pg/storage_test.exs b/integration_test/pg/storage_test.exs
index cd79a3703..b19e2976f 100644
--- a/integration_test/pg/storage_test.exs
+++ b/integration_test/pg/storage_test.exs
@@ -27,8 +27,14 @@ defmodule Ecto.Integration.StorageTest do
     run_psql("DROP DATABASE #{params()[:database]};")
   end
 
-  def create_database do
-    run_psql("CREATE DATABASE #{params()[:database]};")
+  def create_database(owner \\ nil) do
+    query = "CREATE DATABASE #{params()[:database]}"
+    query = if owner do
+      query <> " OWNER #{owner};"
+    else
+      query <> ";"
+    end
+    run_psql(query)
   end
 
   def create_posts do
@@ -74,6 +80,20 @@ defmodule Ecto.Integration.StorageTest do
     drop_database()
   end
 
+  test "storage up with unprivileged user with access to the database" do
+    unprivileged_params = Keyword.merge(params(),
+      username: "unprivileged",
+      password: "pass"
+    )
+    run_psql("CREATE USER unprivileged WITH NOCREATEDB PASSWORD 'pass'")
+    refute Postgres.storage_up(unprivileged_params) == :ok
+    create_database("unprivileged")
+    assert Postgres.storage_up(unprivileged_params) == {:error, :already_up}
+  after
+    run_psql("DROP USER unprivileged")
+    drop_database()
+  end
+
   test "structure dump and load" do
     create_database()
     create_posts()
diff --git a/lib/ecto/adapters/myxql.ex b/lib/ecto/adapters/myxql.ex
index b4b8df768..a12b470f1 100644
--- a/lib/ecto/adapters/myxql.ex
+++ b/lib/ecto/adapters/myxql.ex
@@ -159,19 +159,25 @@ defmodule Ecto.Adapters.MyXQL do
     opts = Keyword.delete(opts, :database)
     charset = opts[:charset] || "utf8mb4"
 
-    command =
-      ~s(CREATE DATABASE `#{database}` DEFAULT CHARACTER SET = #{charset})
-      |> concat_if(opts[:collation], &"DEFAULT COLLATE = #{&1}")
-
-    case run_query(command, opts) do
-      {:ok, _} ->
-        :ok
-      {:error, %{mysql: %{name: :ER_DB_CREATE_EXISTS}}} ->
+    check_existence_command = "SELECT TRUE FROM information_schema.schemata WHERE schema_name = '#{database}'"
+    case run_query(check_existence_command, opts) do
+      {:ok, %{num_rows: 1}} ->
         {:error, :already_up}
-      {:error, error} ->
-        {:error, Exception.message(error)}
-      {:exit, exit} ->
-        {:error, exit_to_exception(exit)}
+      _ ->
+        create_command =
+          ~s(CREATE DATABASE `#{database}` DEFAULT CHARACTER SET = #{charset})
+          |> concat_if(opts[:collation], &"DEFAULT COLLATE = #{&1}")
+
+        case run_query(create_command, opts) do
+          {:ok, _} ->
+            :ok
+          {:error, %{mysql: %{name: :ER_DB_CREATE_EXISTS}}} ->
+            {:error, :already_up}
+          {:error, error} ->
+            {:error, Exception.message(error)}
+          {:exit, exit} ->
+            {:error, exit_to_exception(exit)}
+        end
     end
   end
 
diff --git a/lib/ecto/adapters/postgres.ex b/lib/ecto/adapters/postgres.ex
index 0bc01b162..b702e566d 100644
--- a/lib/ecto/adapters/postgres.ex
+++ b/lib/ecto/adapters/postgres.ex
@@ -127,25 +127,37 @@ defmodule Ecto.Adapters.Postgres do
 
   @impl true
   def storage_up(opts) do
-    database = Keyword.fetch!(opts, :database) || raise ":database is nil in repository configuration"
+    database =
+      Keyword.fetch!(opts, :database) || raise ":database is nil in repository configuration"
+
     encoding = if opts[:encoding] == :unspecified, do: nil, else: opts[:encoding] || "UTF8"
     maintenance_database = Keyword.get(opts, :maintenance_database, @default_maintenance_database)
     opts = Keyword.put(opts, :database, maintenance_database)
 
-    command =
-      ~s(CREATE DATABASE "#{database}")
-      |> concat_if(encoding, &"ENCODING '#{&1}'")
-      |> concat_if(opts[:template], &"TEMPLATE=#{&1}")
-      |> concat_if(opts[:lc_ctype], &"LC_CTYPE='#{&1}'")
-      |> concat_if(opts[:lc_collate], &"LC_COLLATE='#{&1}'")
+    check_existence_command = "SELECT FROM pg_database WHERE datname = '#{database}'"
 
-    case run_query(command, opts) do
-      {:ok, _} ->
-        :ok
-      {:error, %{postgres: %{code: :duplicate_database}}} ->
+    case run_query(check_existence_command, opts) do
+      {:ok, %{num_rows: 1}} ->
         {:error, :already_up}
-      {:error, error} ->
-        {:error, Exception.message(error)}
+
+      _ ->
+        create_command =
+          ~s(CREATE DATABASE "#{database}")
+          |> concat_if(encoding, &"ENCODING '#{&1}'")
+          |> concat_if(opts[:template], &"TEMPLATE=#{&1}")
+          |> concat_if(opts[:lc_ctype], &"LC_CTYPE='#{&1}'")
+          |> concat_if(opts[:lc_collate], &"LC_COLLATE='#{&1}'")
+
+        case run_query(create_command, opts) do
+          {:ok, _} ->
+            :ok
+
+          {:error, %{postgres: %{code: :duplicate_database}}} ->
+            {:error, :already_up}
+
+          {:error, error} ->
+            {:error, Exception.message(error)}
+        end
     end
   end