diff --git a/CHANGELOG.md b/CHANGELOG.md
index 8378fcf3477..9e8374d4c01 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,7 @@ This project adheres to [Semantic Versioning](http://semver.org/).
 - Add support for converting matplotlib reference lines (`axhline`, `axvline`, and horizontal/vertical `axline`) as well as axes-coordinate lines into Plotly layout shapes in `mpl_to_plotly`, including support for date axes [[#5719](https://github.com/plotly/plotly.py/pull/5719)], with thanks to @robertoffmoura for the contribution!
 
 ### Fixed
+- Fix `add_hline` and `add_vline` dropping lines on empty subplots when the target is unambiguous (the grid has a single subplot, or both `row` and `col` are given) [[#5136](https://github.com/plotly/plotly.py/issues/5136)]
 - Fix `mpl_to_plotly` tick marker mirroring, axis positioning, and trace visibility for twinned and overlaid subplots (such as `twinx` and `twiny`) [[#5310](https://github.com/plotly/plotly.py/pull/5310)], with thanks to @robertoffmoura for the contribution!
 - Fix `mpl_to_plotly` losing matplotlib axis line colors by exporting the color of each axis's displayed spine to the plotly x and y axis `linecolor` [[#5311](https://github.com/plotly/plotly.py/pull/5311)], with thanks to @robertoffmoura for the contribution!
 - Fix concurrent first access to lazily initialized graph object properties, which could raise `ValueError("Invalid value")` [[#5691](https://github.com/plotly/plotly.py/pull/5691)], with thanks to @hb1915 for the contribution!
diff --git a/plotly/basedatatypes.py b/plotly/basedatatypes.py
index a7326da8e5a..3292c35bfd6 100644
--- a/plotly/basedatatypes.py
+++ b/plotly/basedatatypes.py
@@ -4050,6 +4050,20 @@ def _process_multiple_axis_spanning_shapes(
                 self.layout[layout_obj][:n_layout_objs_before] + new_layout_objs
             )
 
+    def _axis_spanning_line_target_is_explicit(self, row, col):
+        """
+        Returns True when the subplot targeted by add_hline/add_vline is
+        unambiguous: the grid has a single subplot, or both row and col were
+        given explicitly. In these cases the line is kept even if the
+        subplot does not contain any data yet.
+        """
+        if not self._has_subplots():
+            return False
+        rows, cols = self._get_subplot_rows_columns()
+        if len(rows) * len(cols) == 1:
+            return True
+        return all(rc is not None and rc != "all" for rc in (row, col))
+
     def add_vline(
         self,
         x,
@@ -4064,7 +4078,8 @@ def add_vline(
             row,
             col,
             "vline",
-            exclude_empty_subplots=exclude_empty_subplots,
+            exclude_empty_subplots=exclude_empty_subplots
+            and not self._axis_spanning_line_target_is_explicit(row, col),
             annotation=annotation,
             **kwargs,
         )
@@ -4092,7 +4107,8 @@ def add_hline(
             row,
             col,
             "hline",
-            exclude_empty_subplots=exclude_empty_subplots,
+            exclude_empty_subplots=exclude_empty_subplots
+            and not self._axis_spanning_line_target_is_explicit(row, col),
             annotation=annotation,
             **kwargs,
         )
diff --git a/tests/test_core/test_update_objects/test_update_annotations.py b/tests/test_core/test_update_objects/test_update_annotations.py
index 773ca603b3a..95b022c99b8 100644
--- a/tests/test_core/test_update_objects/test_update_annotations.py
+++ b/tests/test_core/test_update_objects/test_update_annotations.py
@@ -428,3 +428,38 @@ def test_select_annotations_integer(select_annotations_integer):
     assert (len(anns) == 1) and anns[0]["text"] == "B"
     with pytest.raises(IndexError):
         fig.select_annotations(row=2, col=2, selector=3)
+
+
+@pytest.mark.parametrize("method", ["add_hline", "add_vline"])
+def test_axis_spanning_line_kept_on_single_empty_subplot(method):
+    fig = make_subplots(rows=1, cols=1)
+    getattr(fig, method)(1)
+    assert len(fig.layout.shapes) == 1
+
+
+@pytest.mark.parametrize("method", ["add_hline", "add_vline"])
+def test_axis_spanning_line_kept_on_explicit_empty_subplot(method):
+    fig = make_subplots(rows=2, cols=2)
+    getattr(fig, method)(1, row=2, col=1)
+    assert len(fig.layout.shapes) == 1
+    shape = fig.layout.shapes[0]
+    assert (shape.xref, shape.yref) in [("x3", "y3 domain"), ("x3 domain", "y3")]
+
+
+@pytest.mark.parametrize("method", ["add_hline", "add_vline"])
+def test_axis_spanning_line_excludes_unspecified_empty_subplots(method):
+    fig = make_subplots(rows=2, cols=2)
+    getattr(fig, method)(1)
+    getattr(fig, method)(1, row=1)
+    assert len(fig.layout.shapes) == 0
+
+    fig.add_trace(go.Scatter(x=[1, 2], y=[1, 2]), row=1, col=2)
+    getattr(fig, method)(1)
+    assert len(fig.layout.shapes) == 1
+
+
+@pytest.mark.parametrize("method", ["add_hrect", "add_vrect"])
+def test_axis_spanning_rect_still_excluded_on_explicit_empty_subplot(method):
+    fig = make_subplots(rows=2, cols=2)
+    getattr(fig, method)(0, 1, row=2, col=1)
+    assert len(fig.layout.shapes) == 0