diff --git a/Lib/test/pickletester.py b/Lib/test/pickletester.py
index 3a8aee4320c..7c8383f3eaa 100644
--- a/Lib/test/pickletester.py
+++ b/Lib/test/pickletester.py
@@ -73,6 +73,18 @@ class UnseekableIO(io.BytesIO):
         raise io.UnsupportedOperation
 
 
+class MinimalIO(object):
+    """
+    A file-like object that doesn't support readinto().
+    """
+    def __init__(self, *args):
+        self._bio = io.BytesIO(*args)
+        self.getvalue = self._bio.getvalue
+        self.read = self._bio.read
+        self.readline = self._bio.readline
+        self.write = self._bio.write
+
+
 # We can't very well test the extension registry without putting known stuff
 # in it, but we have to be careful to restore its original state.  Code
 # should do this:
@@ -3361,7 +3373,7 @@ class AbstractPicklerUnpicklerObjectTests(unittest.TestCase):
         f.seek(0)
         self.assertEqual(unpickler.load(), data2)
 
-    def _check_multiple_unpicklings(self, ioclass):
+    def _check_multiple_unpicklings(self, ioclass, *, seekable=True):
         for proto in protocols:
             with self.subTest(proto=proto):
                 data1 = [(x, str(x)) for x in range(2000)] + [b"abcde", len]
@@ -3374,10 +3386,10 @@ class AbstractPicklerUnpicklerObjectTests(unittest.TestCase):
                 f = ioclass(pickled * N)
                 unpickler = self.unpickler_class(f)
                 for i in range(N):
-                    if f.seekable():
+                    if seekable:
                         pos = f.tell()
                     self.assertEqual(unpickler.load(), data1)
-                    if f.seekable():
+                    if seekable:
                         self.assertEqual(f.tell(), pos + len(pickled))
                 self.assertRaises(EOFError, unpickler.load)
 
@@ -3385,7 +3397,12 @@ class AbstractPicklerUnpicklerObjectTests(unittest.TestCase):
         self._check_multiple_unpicklings(io.BytesIO)
 
     def test_multiple_unpicklings_unseekable(self):
-        self._check_multiple_unpicklings(UnseekableIO)
+        self._check_multiple_unpicklings(UnseekableIO, seekable=False)
+
+    def test_multiple_unpicklings_minimal(self):
+        # File-like object that doesn't support peek() and readinto()
+        # (bpo-39681)
+        self._check_multiple_unpicklings(MinimalIO, seekable=False)
 
     def test_unpickling_buffering_readline(self):
         # Issue #12687: the unpickler's buffering logic could fail with
diff --git a/Misc/NEWS.d/next/Library/2020-02-21-13-58-40.bpo-39681.zN8hf0.rst b/Misc/NEWS.d/next/Library/2020-02-21-13-58-40.bpo-39681.zN8hf0.rst
new file mode 100644
index 00000000000..c10e2fd7a4b
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-02-21-13-58-40.bpo-39681.zN8hf0.rst
@@ -0,0 +1,2 @@
+Fix a regression where the C pickle module wouldn't allow unpickling from a
+file-like object that doesn't expose a readinto() method.
diff --git a/Modules/_pickle.c b/Modules/_pickle.c
index 9f6e66f70a5..55e2734ca2f 100644
--- a/Modules/_pickle.c
+++ b/Modules/_pickle.c
@@ -1371,13 +1371,42 @@ _Unpickler_ReadInto(UnpicklerObject *self, char *buf, Py_ssize_t n)
     }
 
     /* Read from file */
-    if (!self->readinto) {
+    if (!self->read) {
+        /* We're unpickling memory, this means the input is truncated */
         return bad_readline();
     }
     if (_Unpickler_SkipConsumed(self) < 0) {
         return -1;
     }
 
+    if (!self->readinto) {
+        /* readinto() not supported on file-like object, fall back to read()
+         * and copy into destination buffer (bpo-39681) */
+        PyObject* len = PyLong_FromSsize_t(n);
+        if (len == NULL) {
+            return -1;
+        }
+        PyObject* data = _Pickle_FastCall(self->read, len);
+        if (data == NULL) {
+            return -1;
+        }
+        if (!PyBytes_Check(data)) {
+            PyErr_Format(PyExc_ValueError,
+                         "read() returned non-bytes object (%R)",
+                         Py_TYPE(data));
+            Py_DECREF(data);
+            return -1;
+        }
+        Py_ssize_t read_size = PyBytes_GET_SIZE(data);
+        if (read_size < n) {
+            Py_DECREF(data);
+            return bad_readline();
+        }
+        memcpy(buf, PyBytes_AS_STRING(data), n);
+        Py_DECREF(data);
+        return n;
+    }
+
     /* Call readinto() into user buffer */
     PyObject *buf_obj = PyMemoryView_FromMemory(buf, n, PyBUF_WRITE);
     if (buf_obj == NULL) {
@@ -1606,17 +1635,19 @@ _Unpickler_SetInputStream(UnpicklerObject *self, PyObject *file)
     _Py_IDENTIFIER(readinto);
     _Py_IDENTIFIER(readline);
 
+    /* Optional file methods */
     if (_PyObject_LookupAttrId(file, &PyId_peek, &self->peek) < 0) {
         return -1;
     }
+    if (_PyObject_LookupAttrId(file, &PyId_readinto, &self->readinto) < 0) {
+        return -1;
+    }
     (void)_PyObject_LookupAttrId(file, &PyId_read, &self->read);
-    (void)_PyObject_LookupAttrId(file, &PyId_readinto, &self->readinto);
     (void)_PyObject_LookupAttrId(file, &PyId_readline, &self->readline);
-    if (!self->readline || !self->readinto || !self->read) {
+    if (!self->readline || !self->read) {
         if (!PyErr_Occurred()) {
             PyErr_SetString(PyExc_TypeError,
-                            "file must have 'read', 'readinto' and "
-                            "'readline' attributes");
+                            "file must have 'read' and 'readline' attributes");
         }
         Py_CLEAR(self->read);
         Py_CLEAR(self->readinto);