diff --git a/doc/source/whatsnew/v0.21.1.txt b/doc/source/whatsnew/v0.21.1.txt
index 637ccf0603e0f..33c4aa72c7fd6 100644
--- a/doc/source/whatsnew/v0.21.1.txt
+++ b/doc/source/whatsnew/v0.21.1.txt
@@ -93,7 +93,7 @@ I/O
 Plotting
 ^^^^^^^^
 
--
+- Bug in ``DataFrame.plot()`` and ``Series.plot()`` with :class:`DatetimeIndex` where a figure generated by them is not pickleable in Python 3 (:issue:`18439`)
 -
 -
 
diff --git a/pandas/plotting/_timeseries.py b/pandas/plotting/_timeseries.py
index 3d04973ed0009..56b5311326e98 100644
--- a/pandas/plotting/_timeseries.py
+++ b/pandas/plotting/_timeseries.py
@@ -1,5 +1,7 @@
 # TODO: Use the fact that axis can have units to simplify the process
 
+import functools
+
 import numpy as np
 
 from matplotlib import pylab
@@ -293,6 +295,10 @@ def format_timedelta_ticks(x, pos, n_decimals):
     return s
 
 
+def _format_coord(freq, t, y):
+    return "t = {0}  y = {1:8f}".format(Period(ordinal=int(t), freq=freq), y)
+
+
 def format_dateaxis(subplot, freq, index):
     """
     Pretty-formats the date axis (x-axis).
@@ -327,8 +333,7 @@ def format_dateaxis(subplot, freq, index):
         subplot.xaxis.set_minor_formatter(minformatter)
 
         # x and y coord info
-        subplot.format_coord = lambda t, y: (
-            "t = {0}  y = {1:8f}".format(Period(ordinal=int(t), freq=freq), y))
+        subplot.format_coord = functools.partial(_format_coord, freq)
 
     elif isinstance(index, TimedeltaIndex):
         subplot.xaxis.set_major_formatter(
diff --git a/pandas/tests/plotting/test_datetimelike.py b/pandas/tests/plotting/test_datetimelike.py
index d66012e2a56a0..d6cedac747f25 100644
--- a/pandas/tests/plotting/test_datetimelike.py
+++ b/pandas/tests/plotting/test_datetimelike.py
@@ -1,13 +1,14 @@
 """ Test cases for time series specific (freq conversion, etc) """
 
 from datetime import datetime, timedelta, date, time
+import pickle
 
 import pytest
 from pandas.compat import lrange, zip
 
 import numpy as np
 from pandas import Index, Series, DataFrame, NaT
-from pandas.compat import is_platform_mac
+from pandas.compat import is_platform_mac, PY3
 from pandas.core.indexes.datetimes import date_range, bdate_range
 from pandas.core.indexes.timedeltas import timedelta_range
 from pandas.tseries.offsets import DateOffset
@@ -1470,5 +1471,12 @@ def _check_plot_works(f, freq=None, series=None, *args, **kwargs):
 
         with ensure_clean(return_filelike=True) as path:
             plt.savefig(path)
+
+        # GH18439
+        # this is supported only in Python 3 pickle since
+        # pickle in Python2 doesn't support instancemethod pickling
+        if PY3:
+            with ensure_clean(return_filelike=True) as path:
+                pickle.dump(fig, path)
     finally:
         plt.close(fig)