diff --git a/CHANGELOG.md b/CHANGELOG.md
index 684d02fc8da..442b10026b1 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -57,6 +57,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Fixed warnings being suppressed in `MeanAveragePrecision` when requested ([#2501](https://github.com/Lightning-AI/torchmetrics/pull/2501))
 
 
+- Fixed cornercase in `binary_average_precision` when only negative samples are provided ([#2507](https://github.com/Lightning-AI/torchmetrics/pull/2507))
+
+
 ## [1.3.2] - 2024-03-18
 
 ### Fixed
diff --git a/src/torchmetrics/functional/classification/precision_recall_curve.py b/src/torchmetrics/functional/classification/precision_recall_curve.py
index 64958267737..da12db561a1 100644
--- a/src/torchmetrics/functional/classification/precision_recall_curve.py
+++ b/src/torchmetrics/functional/classification/precision_recall_curve.py
@@ -23,6 +23,7 @@
 from torchmetrics.utilities.compute import _safe_divide, interp
 from torchmetrics.utilities.data import _bincount, _cumsum
 from torchmetrics.utilities.enums import ClassificationTask
+from torchmetrics.utilities.prints import rank_zero_warn
 
 
 def _binary_clf_curve(
@@ -274,6 +275,12 @@ def _binary_precision_recall_curve_compute(
     fps, tps, thresholds = _binary_clf_curve(state[0], state[1], pos_label=pos_label)
     precision = tps / (tps + fps)
     recall = tps / tps[-1]
+    if (state[1] == 0).all():  # all labels are negative, recall is undefined
+        rank_zero_warn(
+            "No positive samples found in target, recall is undefined. Setting recall to one for all thresholds.",
+            UserWarning,
+        )
+        recall = torch.ones_like(recall)
 
     # need to call reversed explicitly, since including that to slice would
     # introduce negative strides that are not yet supported in pytorch
diff --git a/tests/unittests/classification/test_average_precision.py b/tests/unittests/classification/test_average_precision.py
index 2ff0274c93c..51d40839642 100644
--- a/tests/unittests/classification/test_average_precision.py
+++ b/tests/unittests/classification/test_average_precision.py
@@ -143,6 +143,14 @@ def test_binary_average_precision_threshold_arg(self, inputs, threshold_fn):
             assert torch.allclose(ap1, ap2)
 
 
+def test_warning_on_no_positives():
+    """Test that a warning is raised when there are no positive samples in the target."""
+    preds = torch.rand(100)
+    target = torch.zeros(100).long()
+    with pytest.warns(UserWarning, match="No positive samples found in target, recall is undefined. Setting recall.*"):
+        binary_average_precision(preds, target)
+
+
 def _reference_sklearn_avg_precision_multiclass(preds, target, average="macro", ignore_index=None):
     preds = np.moveaxis(preds.numpy(), 1, -1).reshape((-1, preds.shape[1]))
     target = target.numpy().flatten()