diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index c70dfd4f3f6..1a1585596eb 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -48,7 +48,8 @@ Bug fixes
 - Fix a regression where deleting a coordinate from a copied :py:class:`DataArray`
   can affect the original :py:class:`Dataarray`.  (:issue:`3899`, :pull:`3871`)
   By `Todd Jennings <https://github.com/toddrjen>`_
-
+- Fix ``FacetGrid`` when ``vmin == vmax``. (:issue:`3734`)
+  By `Deepak Cherian <https://github.com/dcherian>`_
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/plot/utils.py b/xarray/plot/utils.py
index e6c15037cb8..9fdfcc2c318 100644
--- a/xarray/plot/utils.py
+++ b/xarray/plot/utils.py
@@ -237,18 +237,14 @@ def _determine_cmap_params(
             norm.vmin = vmin
         else:
             if not vmin_was_none and vmin != norm.vmin:
-                raise ValueError(
-                    "Cannot supply vmin and a norm" + " with a different vmin."
-                )
+                raise ValueError("Cannot supply vmin and a norm with a different vmin.")
             vmin = norm.vmin
 
         if norm.vmax is None:
             norm.vmax = vmax
         else:
             if not vmax_was_none and vmax != norm.vmax:
-                raise ValueError(
-                    "Cannot supply vmax and a norm" + " with a different vmax."
-                )
+                raise ValueError("Cannot supply vmax and a norm with a different vmax.")
             vmax = norm.vmax
 
     # if BoundaryNorm, then set levels
@@ -275,6 +271,10 @@ def _determine_cmap_params(
                 levels = ticker.tick_values(vmin, vmax)
         vmin, vmax = levels[0], levels[-1]
 
+    # GH3734
+    if vmin == vmax:
+        vmin, vmax = mpl.ticker.LinearLocator(2).tick_values(vmin, vmax)
+
     if extend is None:
         extend = _determine_extend(calc_data, vmin, vmax)
 
diff --git a/xarray/tests/test_plot.py b/xarray/tests/test_plot.py
index 7f3f1620133..46556c14517 100644
--- a/xarray/tests/test_plot.py
+++ b/xarray/tests/test_plot.py
@@ -833,10 +833,10 @@ def test_norm_sets_vmin_vmax(self):
 
         for norm, extend in zip(
             [
-                mpl.colors.LogNorm(),
-                mpl.colors.LogNorm(vmin + 1, vmax - 1),
-                mpl.colors.LogNorm(None, vmax - 1),
-                mpl.colors.LogNorm(vmin + 1, None),
+                mpl.colors.Normalize(),
+                mpl.colors.Normalize(vmin + 0.1, vmax - 0.1),
+                mpl.colors.Normalize(None, vmax - 0.1),
+                mpl.colors.Normalize(vmin + 0.1, None),
             ],
             ["neither", "both", "max", "min"],
         ):
@@ -1752,6 +1752,13 @@ def test_can_set_vmin_vmax(self):
             clim = np.array(image.get_clim())
             assert np.allclose(expected, clim)
 
+    @pytest.mark.slow
+    def test_vmin_vmax_equal(self):
+        # regression test for GH3734
+        fg = self.g.map_dataarray(xplt.imshow, "x", "y", vmin=50, vmax=50)
+        for mappable in fg._mappables:
+            assert mappable.norm.vmin != mappable.norm.vmax
+
     @pytest.mark.slow
     @pytest.mark.filterwarnings("ignore")
     def test_can_set_norm(self):