diff --git a/pandas/plotting/_matplotlib/timeseries.py b/pandas/plotting/_matplotlib/timeseries.py
index 9d8c26093296e..475452c71db58 100644
--- a/pandas/plotting/_matplotlib/timeseries.py
+++ b/pandas/plotting/_matplotlib/timeseries.py
@@ -7,6 +7,7 @@
 
 from pandas._libs.tslibs import Period, to_offset
 from pandas._libs.tslibs.frequencies import FreqGroup, base_and_stride, get_freq_code
+from pandas._typing import FrameOrSeriesUnion
 
 from pandas.core.dtypes.generic import (
     ABCDatetimeIndex,
@@ -192,7 +193,7 @@ def _get_freq(ax, series: "Series"):
     return freq, ax_freq
 
 
-def _use_dynamic_x(ax, data):
+def _use_dynamic_x(ax, data: "FrameOrSeriesUnion") -> bool:
     freq = _get_index_freq(data.index)
     ax_freq = _get_ax_freq(ax)
 
diff --git a/pandas/tests/plotting/test_datetimelike.py b/pandas/tests/plotting/test_datetimelike.py
index 7dcb692e29337..738df5244955a 100644
--- a/pandas/tests/plotting/test_datetimelike.py
+++ b/pandas/tests/plotting/test_datetimelike.py
@@ -16,7 +16,7 @@
 from pandas.core.resample import DatetimeIndex
 from pandas.tests.plotting.common import TestPlotBase
 
-from pandas.tseries.offsets import DateOffset
+from pandas.tseries.offsets import DateOffset, WeekOfMonth
 
 
 @td.skip_if_no_mpl
@@ -325,6 +325,18 @@ def test_business_freq_convert(self):
         idx = ax.get_lines()[0].get_xdata()
         assert PeriodIndex(data=idx).freqstr == "M"
 
+    def test_freq_with_no_period_alias(self):
+        # GH34487
+        freq = WeekOfMonth()
+        bts = tm.makeTimeSeries(5).asfreq(freq)
+        _, ax = self.plt.subplots()
+        bts.plot(ax=ax)
+        assert ax.get_lines()[0].get_xydata()[0, 0] == bts.index[0].toordinal()
+        idx = ax.get_lines()[0].get_xdata()
+        msg = "freq not specified and cannot be inferred"
+        with pytest.raises(ValueError, match=msg):
+            PeriodIndex(data=idx)
+
     def test_nonzero_base(self):
         # GH2571
         idx = date_range("2012-12-20", periods=24, freq="H") + timedelta(minutes=30)