diff --git a/sklearn/cluster/tests/test_hdbscan.py b/sklearn/cluster/tests/test_hdbscan.py
index c0c281ce31475..8f4629f573842 100644
--- a/sklearn/cluster/tests/test_hdbscan.py
+++ b/sklearn/cluster/tests/test_hdbscan.py
@@ -287,22 +287,37 @@ def test_hdbscan_precomputed_non_brute(tree):
 def test_hdbscan_sparse():
     """
     Tests that HDBSCAN works correctly when passing sparse feature data.
+    Evaluates correctness by comparing against the same data passed as a dense
+    array.
     """
-    sparse_X = sparse.csr_matrix(X)
 
-    labels = HDBSCAN().fit(sparse_X).labels_
-    n_clusters = len(set(labels) - OUTLIER_SET)
+    dense_labels = HDBSCAN().fit(X).labels_
+    n_clusters = len(set(dense_labels) - OUTLIER_SET)
     assert n_clusters == 3
 
-    sparse_X_nan = sparse_X.copy()
-    sparse_X_nan[0, 0] = np.nan
-    labels = HDBSCAN().fit(sparse_X_nan).labels_
-    n_clusters = len(set(labels) - OUTLIER_SET)
-    assert n_clusters == 3
+    _X_sparse = sparse.csr_matrix(X)
+    X_sparse = _X_sparse.copy()
+    sparse_labels = HDBSCAN().fit(X_sparse).labels_
+    assert_array_equal(dense_labels, sparse_labels)
+
+    # Compare that the sparse and dense non-precomputed routines return the same labels
+    # where the 0th observation contains the outlier.
+    for outlier_val, outlier_type in ((np.inf, "infinite"), (np.nan, "missing")):
+        X_dense = X.copy()
+        X_dense[0, 0] = outlier_val
+        dense_labels = HDBSCAN().fit(X_dense).labels_
+        n_clusters = len(set(dense_labels) - OUTLIER_SET)
+        assert n_clusters == 3
+        assert dense_labels[0] == _OUTLIER_ENCODING[outlier_type]["label"]
+
+        X_sparse = _X_sparse.copy()
+        X_sparse[0, 0] = outlier_val
+        sparse_labels = HDBSCAN().fit(X_sparse).labels_
+        assert_array_equal(dense_labels, sparse_labels)
 
     msg = "Sparse data matrices only support algorithm `brute`."
     with pytest.raises(ValueError, match=msg):
-        HDBSCAN(metric="euclidean", algorithm="balltree").fit(sparse_X)
+        HDBSCAN(metric="euclidean", algorithm="balltree").fit(X_sparse)
 
 
 @pytest.mark.parametrize("algorithm", ALGORITHMS)