diff --git a/doc/whats_new/v1.4.rst b/doc/whats_new/v1.4.rst
index e6a57bd551317..4994432df8034 100644
--- a/doc/whats_new/v1.4.rst
+++ b/doc/whats_new/v1.4.rst
@@ -110,6 +110,13 @@ Changelog
   object in the parameter grid if it's an estimator. :pr:`26786` by `Adrin
   Jalali`_.
 
+:mod:`sklearn.neighbors`
+........................
+
+- |Fix| Neighbors based estimators now correctly work when `metric="minkowski"` and the
+  metric parameter `p` is in the range `0 < p < 1`, regardless of the `dtype` of `X`.
+  :pr:`26760` by :user:`Shreesha Kumar Bhat <Shreesha3112>`.
+
 :mod:`sklearn.tree`
 ...................
 
diff --git a/sklearn/metrics/_dist_metrics.pyx.tp b/sklearn/metrics/_dist_metrics.pyx.tp
index bc54e51a7511a..43497c9c50cee 100644
--- a/sklearn/metrics/_dist_metrics.pyx.tp
+++ b/sklearn/metrics/_dist_metrics.pyx.tp
@@ -1271,19 +1271,27 @@ cdef class MinkowskiDistance{{name_suffix}}(DistanceMetric{{name_suffix}}):
 
     Parameters
     ----------
-    p : int
+    p : float
         The order of the p-norm of the difference (see above).
+
+        .. versionchanged:: 1.4.0
+            Minkowski distance allows `p` to be `0<p<1`.
+
+
     w : (N,) array-like (optional)
         The weight vector.
 
-    Minkowski Distance requires p >= 1 and finite. For p = infinity,
-    use ChebyshevDistance.
+    Minkowski Distance requires p > 0 and finite.
+    When :math:`p \in (0,1)`, it isn't a true metric but is permissible when
+    the triangular inequality isn't necessary.
+    For p = infinity, use ChebyshevDistance.
     Note that for p=1, ManhattanDistance is more efficient, and for
     p=2, EuclideanDistance is more efficient.
+
     """
     def __init__(self, p, w=None):
-        if p < 1:
-            raise ValueError("p must be greater than 1")
+        if p <= 0:
+            raise ValueError("p must be greater than 0")
         elif np.isinf(p):
             raise ValueError("MinkowskiDistance requires finite p. "
                              "For p=inf, use ChebyshevDistance.")
diff --git a/sklearn/metrics/tests/test_dist_metrics.py b/sklearn/metrics/tests/test_dist_metrics.py
index 16aa5c569b161..be5d12f0414b8 100644
--- a/sklearn/metrics/tests/test_dist_metrics.py
+++ b/sklearn/metrics/tests/test_dist_metrics.py
@@ -15,6 +15,7 @@
 )
 from sklearn.utils import check_random_state
 from sklearn.utils._testing import assert_allclose, create_memmap_backed_data
+from sklearn.utils.fixes import parse_version, sp_version
 
 
 def dist_func(x1, x2, p):
@@ -42,18 +43,17 @@ def dist_func(x1, x2, p):
 V = rng.random_sample((d, d))
 VI = np.dot(V, V.T)
 
-
 METRICS_DEFAULT_PARAMS = [
     ("euclidean", {}),
     ("cityblock", {}),
-    ("minkowski", dict(p=(1, 1.5, 2, 3))),
+    ("minkowski", dict(p=(0.5, 1, 1.5, 2, 3))),
     ("chebyshev", {}),
     ("seuclidean", dict(V=(rng.random_sample(d),))),
     ("mahalanobis", dict(VI=(VI,))),
     ("hamming", {}),
     ("canberra", {}),
     ("braycurtis", {}),
-    ("minkowski", dict(p=(1, 1.5, 3), w=(rng.random_sample(d),))),
+    ("minkowski", dict(p=(0.5, 1, 1.5, 3), w=(rng.random_sample(d),))),
 ]
 
 
@@ -76,6 +76,13 @@ def test_cdist(metric_param_grid, X, Y):
             # with scipy
             rtol_dict = {"rtol": 1e-6}
 
+        # TODO: Remove when scipy minimum version >= 1.7.0
+        # scipy supports 0<p<1 for minkowski metric >= 1.7.0
+        if metric == "minkowski":
+            p = kwargs["p"]
+            if sp_version < parse_version("1.7.0") and p < 1:
+                pytest.skip("scipy does not support 0<p<1 for minkowski metric < 1.7.0")
+
         D_scipy_cdist = cdist(X, Y, metric, **kwargs)
 
         dm = DistanceMetric.get_metric(metric, X.dtype, **kwargs)
@@ -150,6 +157,12 @@ def test_pdist(metric_param_grid, X):
             # with scipy
             rtol_dict = {"rtol": 1e-6}
 
+        # TODO: Remove when scipy minimum version >= 1.7.0
+        # scipy supports 0<p<1 for minkowski metric >= 1.7.0
+        if metric == "minkowski":
+            p = kwargs["p"]
+            if sp_version < parse_version("1.7.0") and p < 1:
+                pytest.skip("scipy does not support 0<p<1 for minkowski metric < 1.7.0")
         D_scipy_pdist = cdist(X, X, metric, **kwargs)
 
         dm = DistanceMetric.get_metric(metric, X.dtype, **kwargs)
@@ -397,3 +410,9 @@ def test_get_metric_bad_dtype():
     msg = r"Unexpected dtype .* provided. Please select a dtype from"
     with pytest.raises(ValueError, match=msg):
         DistanceMetric.get_metric("manhattan", dtype)
+
+
+def test_minkowski_metric_validate_bad_p_parameter():
+    msg = "p must be greater than 0"
+    with pytest.raises(ValueError, match=msg):
+        DistanceMetric.get_metric("minkowski", p=0)
diff --git a/sklearn/neighbors/tests/test_neighbors.py b/sklearn/neighbors/tests/test_neighbors.py
index 405ac3a6d0847..d24fc618d184c 100644
--- a/sklearn/neighbors/tests/test_neighbors.py
+++ b/sklearn/neighbors/tests/test_neighbors.py
@@ -2207,3 +2207,22 @@ def test_predict_dataframe():
 
     knn = neighbors.KNeighborsClassifier(n_neighbors=2).fit(X, y)
     knn.predict(X)
+
+
+def test_nearest_neighbours_works_with_p_less_than_1():
+    """Check that NearestNeighbors works with :math:`p \\in (0,1)` when `algorithm`
+    is `"auto"` or `"brute"` regardless of the dtype of X.
+
+    Non-regression test for issue #26548
+    """
+    X = np.array([[1.0, 0.0], [0.0, 0.0], [0.0, 1.0]])
+    neigh = neighbors.NearestNeighbors(
+        n_neighbors=3, algorithm="brute", metric_params={"p": 0.5}
+    )
+    neigh.fit(X)
+
+    y = neigh.radius_neighbors(X[0].reshape(1, -1), radius=4, return_distance=False)
+    assert_allclose(y[0], [0, 1, 2])
+
+    y = neigh.kneighbors(X[0].reshape(1, -1), return_distance=False)
+    assert_allclose(y[0], [0, 1, 2])