diff --git a/_pytest/fixtures.py b/_pytest/fixtures.py
index 1a6e245c75b..64d21b9f696 100644
--- a/_pytest/fixtures.py
+++ b/_pytest/fixtures.py
@@ -733,10 +733,19 @@ def addfinalizer(self, finalizer):
         self._finalizer.append(finalizer)
 
     def finish(self):
+        exceptions = []
         try:
             while self._finalizer:
-                func = self._finalizer.pop()
-                func()
+                try:
+                    func = self._finalizer.pop()
+                    func()
+                except:
+                    exceptions.append(sys.exc_info())
+            if exceptions:
+                e = exceptions[0]
+                del exceptions  # ensure we don't keep all frames alive because of the traceback
+                py.builtin._reraise(*e)
+
         finally:
             ihook = self._fixturemanager.session.ihook
             ihook.pytest_fixture_post_finalizer(fixturedef=self)
diff --git a/changelog/2440.bugfix b/changelog/2440.bugfix
new file mode 100644
index 00000000000..7f1f7d50406
--- /dev/null
+++ b/changelog/2440.bugfix
@@ -0,0 +1 @@
+Exceptions raised during teardown by finalizers are now suppressed until all finalizers are called, with the initial exception reraised.
diff --git a/testing/python/fixture.py b/testing/python/fixture.py
index 4c9ad7a9185..1e58a555046 100644
--- a/testing/python/fixture.py
+++ b/testing/python/fixture.py
@@ -657,6 +657,39 @@ def test_second():
             "*1 error*"  # XXX the whole module collection fails
             ])
 
+    def test_request_subrequest_addfinalizer_exceptions(self, testdir):
+        """
+        Ensure exceptions raised during teardown by a finalizer are suppressed
+        until all finalizers are called, re-raising the first exception (#2440)
+        """
+        testdir.makepyfile("""
+            import pytest
+            l = []
+            def _excepts(where):
+                raise Exception('Error in %s fixture' % where)
+            @pytest.fixture
+            def subrequest(request):
+                return request
+            @pytest.fixture
+            def something(subrequest):
+                subrequest.addfinalizer(lambda: l.append(1))
+                subrequest.addfinalizer(lambda: l.append(2))
+                subrequest.addfinalizer(lambda: _excepts('something'))
+            @pytest.fixture
+            def excepts(subrequest):
+                subrequest.addfinalizer(lambda: _excepts('excepts'))
+                subrequest.addfinalizer(lambda: l.append(3))
+            def test_first(something, excepts):
+                pass
+            def test_second():
+                assert l == [3, 2, 1]
+        """)
+        result = testdir.runpytest()
+        result.stdout.fnmatch_lines([
+            '*Exception: Error in excepts fixture',
+            '* 2 passed, 1 error in *',
+        ])
+
     def test_request_getmodulepath(self, testdir):
         modcol = testdir.getmodulecol("def test_somefunc(): pass")
         item, = testdir.genitems([modcol])