diff --git a/doc/api/next_api_changes/deprecations/19341-TH.rst b/doc/api/next_api_changes/deprecations/19341-TH.rst
new file mode 100644
index 000000000000..07ab5bdde4b8
--- /dev/null
+++ b/doc/api/next_api_changes/deprecations/19341-TH.rst
@@ -0,0 +1,5 @@
+``MarkerStyle`` is considered immutable
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+``MarkerStyle.set_fillstyle()`` and ``MarkerStyle.set_marker()`` are
+deprecated. Create a new ``MarkerStyle`` with the respective parameters
+instead.
diff --git a/lib/matplotlib/lines.py b/lib/matplotlib/lines.py
index bac48f3522c2..6d2d196a3e32 100644
--- a/lib/matplotlib/lines.py
+++ b/lib/matplotlib/lines.py
@@ -534,7 +534,7 @@ def set_fillstyle(self, fs):
 
             For examples see :ref:`marker_fill_styles`.
         """
-        self._marker.set_fillstyle(fs)
+        self.set_marker(MarkerStyle(self._marker.get_marker(), fs))
         self.stale = True
 
     def set_markevery(self, every):
@@ -930,7 +930,8 @@ def get_markeredgecolor(self):
             if rcParams['_internal.classic_mode']:
                 if self._marker.get_marker() in ('.', ','):
                     return self._color
-                if self._marker.is_filled() and self.get_fillstyle() != 'none':
+                if (self._marker.is_filled()
+                        and self._marker.get_fillstyle() != 'none'):
                     return 'k'  # Bad hard-wired default...
             return self._color
         else:
@@ -945,7 +946,7 @@ def get_markeredgewidth(self):
         return self._markeredgewidth
 
     def _get_markerfacecolor(self, alt=False):
-        if self.get_fillstyle() == 'none':
+        if self._marker.get_fillstyle() == 'none':
             return 'none'
         fc = self._markerfacecoloralt if alt else self._markerfacecolor
         if cbook._str_lower_equal(fc, 'auto'):
@@ -1166,7 +1167,7 @@ def set_marker(self, marker):
             See `~matplotlib.markers` for full description of possible
             arguments.
         """
-        self._marker.set_marker(marker)
+        self._marker = MarkerStyle(marker, self._marker.get_fillstyle())
         self.stale = True
 
     def set_markeredgecolor(self, ec):
diff --git a/lib/matplotlib/markers.py b/lib/matplotlib/markers.py
index 403321b38c70..67e00ac261fa 100644
--- a/lib/matplotlib/markers.py
+++ b/lib/matplotlib/markers.py
@@ -147,6 +147,9 @@ class MarkerStyle:
     """
     A class representing marker types.
 
+    Instances are immutable. If you need to change anything, create a new
+    instance.
+
     Attributes
     ----------
     markers : list
@@ -228,8 +231,8 @@ def __init__(self, marker=None, fillstyle=None):
             One of 'full', 'left', 'right', 'bottom', 'top', 'none'.
         """
         self._marker_function = None
-        self.set_fillstyle(fillstyle)
-        self.set_marker(marker)
+        self._set_fillstyle(fillstyle)
+        self._set_marker(marker)
 
     def _recache(self):
         if self._marker_function is None:
@@ -256,7 +259,11 @@ def is_filled(self):
     def get_fillstyle(self):
         return self._fillstyle
 
+    @_api.deprecated("3.4", alternative="a new marker")
     def set_fillstyle(self, fillstyle):
+        return self._set_fillstyle(fillstyle)
+
+    def _set_fillstyle(self, fillstyle):
         """
         Set the fillstyle.
 
@@ -281,7 +288,11 @@ def get_capstyle(self):
     def get_marker(self):
         return self._marker
 
+    @_api.deprecated("3.4", alternative="a new marker")
     def set_marker(self, marker):
+        return self._set_marker(marker)
+
+    def _set_marker(self, marker):
         """
         Set the marker.
 
diff --git a/lib/matplotlib/tests/test_marker.py b/lib/matplotlib/tests/test_marker.py
index 1ac7aaa0d0d8..f85d4ff467ef 100644
--- a/lib/matplotlib/tests/test_marker.py
+++ b/lib/matplotlib/tests/test_marker.py
@@ -13,27 +13,43 @@ def test_marker_fillstyle():
     assert not marker_style.is_filled()
 
 
-def test_markers_valid():
-    marker_style = markers.MarkerStyle()
-    mrk_array = np.array([[-0.5, 0],
-                          [0.5, 0]])
+@pytest.mark.parametrize('marker', [
+    'o',
+    'x',
+    '',
+    'None',
+    None,
+    r'$\frac{1}{2}$',
+    "$\u266B$",
+    1,
+    markers.TICKLEFT,
+    [[-1, 0], [1, 0]],
+    np.array([[-1, 0], [1, 0]]),
+    Path([[0, 0], [1, 0]], [Path.MOVETO, Path.LINETO]),
+    (5, 0),  # a pentagon
+    (7, 1),  # a 7-pointed star
+    (5, 2),  # asterisk
+    (5, 0, 10),  # a pentagon, rotated by 10 degrees
+    (7, 1, 10),  # a 7-pointed star, rotated by 10 degrees
+    (5, 2, 10),  # asterisk, rotated by 10 degrees
+    markers.MarkerStyle(),
+    markers.MarkerStyle('o'),
+])
+def test_markers_valid(marker):
     # Checking this doesn't fail.
-    marker_style.set_marker(mrk_array)
+    markers.MarkerStyle(marker)
 
 
-def test_markers_invalid():
-    marker_style = markers.MarkerStyle()
-    mrk_array = np.array([[-0.5, 0, 1, 2, 3]])
-    # Checking this does fail.
+@pytest.mark.parametrize('marker', [
+    'square',  # arbitrary string
+    np.array([[-0.5, 0, 1, 2, 3]]),  # 1D array
+    (1,),
+    (5, 3),  # second parameter of tuple must be 0, 1, or 2
+    (1, 2, 3, 4),
+])
+def test_markers_invalid(marker):
     with pytest.raises(ValueError):
-        marker_style.set_marker(mrk_array)
-
-
-def test_marker_path():
-    marker_style = markers.MarkerStyle()
-    path = Path([[0, 0], [1, 0]], [Path.MOVETO, Path.LINETO])
-    # Checking this doesn't fail.
-    marker_style.set_marker(path)
+        markers.MarkerStyle(marker)
 
 
 class UnsnappedMarkerStyle(markers.MarkerStyle):