diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 41d519e0765dc..bdd0f1b886350 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -803,7 +803,7 @@ Plotting
 - Bug in :meth:`DataFrame.boxplot` and :meth:`DataFrame.plot.boxplot` lost color attributes of ``medianprops``, ``whiskerprops``, ``capprops`` and ``medianprops`` (:issue:`30346`)
 - Bug in :meth:`DataFrame.hist` where the order of ``column`` argument was ignored (:issue:`29235`)
 - Bug in :meth:`DataFrame.plot.scatter` that when adding multiple plots with different ``cmap``, colorbars alway use the first ``cmap`` (:issue:`33389`)
-
+- Bug in :meth:`DataFrame.plot.scatter` was adding a colorbar to the plot even if the argument `c` was assigned to a column containing color names (:issue:`34316`)
 
 Groupby/resample/rolling
 ^^^^^^^^^^^^^^^^^^^^^^^^
diff --git a/pandas/plotting/_matplotlib/core.py b/pandas/plotting/_matplotlib/core.py
index a049ac99f0e08..622d9e18a4434 100644
--- a/pandas/plotting/_matplotlib/core.py
+++ b/pandas/plotting/_matplotlib/core.py
@@ -13,6 +13,7 @@
     is_iterator,
     is_list_like,
     is_number,
+    is_numeric_dtype,
 )
 from pandas.core.dtypes.generic import (
     ABCDataFrame,
@@ -951,9 +952,6 @@ def _make_plot(self):
 
         c_is_column = is_hashable(c) and c in self.data.columns
 
-        # plot a colorbar only if a colormap is provided or necessary
-        cb = self.kwds.pop("colorbar", self.colormap or c_is_column)
-
         # pandas uses colormap, matplotlib uses cmap.
         cmap = self.colormap or "Greys"
         cmap = self.plt.cm.get_cmap(cmap)
@@ -969,6 +967,12 @@ def _make_plot(self):
         else:
             c_values = c
 
+        # plot colorbar if
+        # 1. colormap is assigned, and
+        # 2.`c` is a column containing only numeric values
+        plot_colorbar = self.colormap or c_is_column
+        cb = self.kwds.pop("colorbar", is_numeric_dtype(c_values) and plot_colorbar)
+
         if self.legend and hasattr(self, "label"):
             label = self.label
         else:
diff --git a/pandas/tests/plotting/test_frame.py b/pandas/tests/plotting/test_frame.py
index c84a09f21f46b..8992e27a78d6b 100644
--- a/pandas/tests/plotting/test_frame.py
+++ b/pandas/tests/plotting/test_frame.py
@@ -1306,6 +1306,17 @@ def test_plot_scatter_with_c(self):
         float_array = np.array([0.0, 1.0])
         df.plot.scatter(x="A", y="B", c=float_array, cmap="spring")
 
+    @pytest.mark.parametrize("cmap", [None, "Greys"])
+    def test_scatter_with_c_column_name_with_colors(self, cmap):
+        # https://github.com/pandas-dev/pandas/issues/34316
+        df = pd.DataFrame(
+            [[5.1, 3.5], [4.9, 3.0], [7.0, 3.2], [6.4, 3.2], [5.9, 3.0]],
+            columns=["length", "width"],
+        )
+        df["species"] = ["r", "r", "g", "g", "b"]
+        ax = df.plot.scatter(x=0, y=1, c="species", cmap=cmap)
+        assert ax.collections[0].colorbar is None
+
     def test_plot_scatter_with_s(self):
         # this refers to GH 32904
         df = DataFrame(np.random.random((10, 3)) * 100, columns=["a", "b", "c"],)