diff --git a/rich/console.py b/rich/console.py
index 994adfc0..406a088c 100644
--- a/rich/console.py
+++ b/rich/console.py
@@ -1723,12 +1723,13 @@ class Console:
                 for renderable in renderables:
                     extend(render(renderable, render_options))
             else:
+                render_style = self.get_style(style)
+                new_line = Segment.line()
                 for renderable in renderables:
-                    extend(
-                        Segment.apply_style(
-                            render(renderable, render_options), self.get_style(style)
-                        )
-                    )
+                    for line in Segment.split_lines(render(renderable, render_options)):
+                        extend(Segment.apply_style(line, render_style))
+                        new_segments.append(new_line)
+
             if new_line_start:
                 if (
                     len("".join(segment.text for segment in new_segments).splitlines())
diff --git a/tests/test_text.py b/tests/test_text.py
index b528608a..b6d39f59 100644
--- a/tests/test_text.py
+++ b/tests/test_text.py
@@ -1110,3 +1110,20 @@ def test_soft_wrap() -> None:
     print(repr(output))
     expected = "\x1b[37;44m Hello World \x1b[0m\n"
     assert output == expected
+
+
+def test_soft_wrap_styled() -> None:
+    """Regression test for https://github.com/Textualize/rich/issues/3838
+
+    If soft_wrap is True and a style is set, we don't want to style the new lines.
+    """
+    console = Console(color_system="standard", width=80, force_terminal=True)
+    with console.capture() as capture:
+        console.print("soft wrap is on", style="blue on white", soft_wrap=True)
+        console.print("Next line")
+
+    output = capture.get()
+    print(repr(output))
+    # Background is reset before \n
+    expected = "\x1b[34;47msoft wrap is on\x1b[0m\nNext line\n"
+    assert output == expected