diff --git a/isort/core.py b/isort/core.py
index d763ad469..9f577dac6 100644
--- a/isort/core.py
+++ b/isort/core.py
@@ -13,7 +13,8 @@
 
 CIMPORT_IDENTIFIERS = ("cimport ", "cimport*", "from.cimport")
 IMPORT_START_IDENTIFIERS = ("from ", "from.import", "import ", "import*") + CIMPORT_IDENTIFIERS
-COMMENT_INDICATORS = ('"""', "'''", "'", '"', "#")
+DOCSTRING_INDICATORS = ('"""', "'''")
+COMMENT_INDICATORS = DOCSTRING_INDICATORS + ("'", '"', "#")
 CODE_SORT_COMMENTS = (
     "# isort: list",
     "# isort: dict",
@@ -317,6 +318,7 @@ def process(
                 and not in_quote
                 and not import_section
                 and not line.lstrip().startswith(COMMENT_INDICATORS)
+                and not line.rstrip().endswith(DOCSTRING_INDICATORS)
             ):
                 import_section = line_separator.join(add_imports) + line_separator
                 if end_of_file and index != 0:
diff --git a/tests/unit/test_isort.py b/tests/unit/test_isort.py
index 19452db6d..7a02884ba 100644
--- a/tests/unit/test_isort.py
+++ b/tests/unit/test_isort.py
@@ -873,6 +873,41 @@ def test_add_imports() -> None:
         "    pass\n"
     )
 
+    # On a file that has no pre-existing imports and a multiline docstring
+    test_input = (
+        '"""Module docstring\n\nWith a second line\n"""\n' "class MyClass(object):\n    pass\n"
+    )
+    test_output = isort.code(code=test_input, add_imports=["from __future__ import print_function"])
+    assert test_output == (
+        '"""Module docstring\n'
+        "\n"
+        "With a second line\n"
+        '"""\n'
+        "from __future__ import print_function\n"
+        "\n"
+        "\n"
+        "class MyClass(object):\n"
+        "    pass\n"
+    )
+
+    # On a file that has no pre-existing imports and a multiline docstring.
+    # In this example, the closing quotes for the docstring are on the final
+    # line rather than a separate one.
+    test_input = (
+        '"""Module docstring\n\nWith a second line"""\n' "class MyClass(object):\n    pass\n"
+    )
+    test_output = isort.code(code=test_input, add_imports=["from __future__ import print_function"])
+    assert test_output == (
+        '"""Module docstring\n'
+        "\n"
+        'With a second line"""\n'
+        "from __future__ import print_function\n"
+        "\n"
+        "\n"
+        "class MyClass(object):\n"
+        "    pass\n"
+    )
+
     # On a file that has no pre-existing imports, and no doc-string
     test_input = "class MyClass(object):\n    pass\n"
     test_output = isort.code(code=test_input, add_imports=["from __future__ import print_function"])