diff --git a/Lib/_pyio.py b/Lib/_pyio.py
index 654a69c..334c2b7 100644
--- a/Lib/_pyio.py
+++ b/Lib/_pyio.py
@@ -1696,6 +1696,7 @@
         return cookie
 
     def read(self, n=None):
+        self._checkReadable()
         if n is None:
             n = -1
         decoder = self._decoder or self._get_decoder()
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index d5be405..53017f3 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -1754,6 +1754,13 @@
             self.assertEquals(f.read(), data * 2)
             self.assertEquals(buf.getvalue(), (data * 2).encode(encoding))
 
+    def test_unreadable(self):
+        class UnReadable(self.BytesIO):
+            def readable(self):
+                return False
+        txt = self.TextIOWrapper(UnReadable())
+        self.assertRaises(IOError, txt.read)
+
     def test_read_one_by_one(self):
         txt = self.TextIOWrapper(self.BytesIO(b"AA\r\nBB"))
         reads = ""
diff --git a/Misc/NEWS b/Misc/NEWS
index 78adb64..914e257 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -53,6 +53,8 @@
 Library
 -------
 
+- Issue #5628: Fix io.TextIOWrapper.read() with a unreadable buffer.
+
 - Issue #5619: Multiprocessing children disobey the debug flag and causes
   popups on windows buildbots. Patch applied to work around this issue.
 
diff --git a/Modules/_textio.c b/Modules/_textio.c
index dbfc8ae..cc229a8 100644
--- a/Modules/_textio.c
+++ b/Modules/_textio.c
@@ -1348,6 +1348,11 @@
 
     CHECK_CLOSED(self);
 
+    if (self->decoder == NULL) {
+        PyErr_SetString(PyExc_IOError, "not readable");
+        return NULL;
+    }
+
     if (_TextIOWrapper_writeflush(self) < 0)
         return NULL;