diff --git a/folium/features.py b/folium/features.py
index 587f5e053b..2a38e74c57 100644
--- a/folium/features.py
+++ b/folium/features.py
@@ -1888,7 +1888,8 @@ class CustomIcon(Icon):
         * Otherwise a string will be assumed to be JSON and embedded.
         * If array-like, it will be converted to PNG base64 string and embedded.
     icon_size : tuple of 2 int, optional
-        Size of the icon image in pixels.
+        Size of the icon image in pixels. If not given, the image is shown
+        at its natural size.
     icon_anchor : tuple of 2 int, optional
         The coordinates of the "tip" of the icon
         (relative to its top left corner).
diff --git a/folium/map.py b/folium/map.py
index daf7ee84cb..7f08da9884 100644
--- a/folium/map.py
+++ b/folium/map.py
@@ -509,8 +509,21 @@ class Marker(MacroElement):
     class SetIcon(MacroElement):
         """Set the icon of a marker after both are created."""
 
+        # Leaflet reuses the current <img> element when the new icon is also an
+        # image, and keeps its inline size and margins if the new icon does not
+        # set them. Clear them first, so an icon without `icon_size` keeps the
+        # natural size of its image instead of the size of the default icon.
         _template = Template("""
             {% macro script(this, kwargs) %}
+                {
+                    const element = {{ this.marker.get_name() }}.getElement();
+                    if (element) {
+                        element.style.width = "";
+                        element.style.height = "";
+                        element.style.marginLeft = "";
+                        element.style.marginTop = "";
+                    }
+                }
                 {{ this.marker.get_name() }}.setIcon({{ this.icon.get_name() }});
             {% endmacro %}
         """)
diff --git a/tests/test_map.py b/tests/test_map.py
index 594c42ce0e..1cebf9c2fb 100644
--- a/tests/test_map.py
+++ b/tests/test_map.py
@@ -305,6 +305,24 @@ def test_marker_numpy_array_as_location():
     Marker(np.array([0, 0]))
 
 
+def test_set_icon_clears_size_of_previous_icon():
+    # Leaflet reuses the <img> of the default icon, so its inline size must be
+    # cleared for a custom icon without icon_size to keep its natural size.
+    from folium.features import CustomIcon
+
+    m = Map()
+    marker = Marker([0, 0], icon=CustomIcon("https://example.com/logo.png"))
+    marker.add_to(m)
+    script = normalize(m.get_root().render())
+    element = f"{marker.get_name()}.getElement()"
+    set_icon = f"{marker.get_name()}.setIcon({marker.icon.get_name()});"
+    assert element in script
+    assert set_icon in script
+    assert script.index(element) < script.index(set_icon)
+    for prop in ("width", "height", "marginLeft", "marginTop"):
+        assert f'.style.{prop} = "";' in script
+
+
 def test_icon_hex_marker_color():
     with warnings.catch_warnings():
         warnings.simplefilter("error")