diff --git a/sklearn/metrics/_dist_metrics.pyx.tp b/sklearn/metrics/_dist_metrics.pyx.tp
index 6b5ea300f038b..eb9b1a46c4d1f 100644
--- a/sklearn/metrics/_dist_metrics.pyx.tp
+++ b/sklearn/metrics/_dist_metrics.pyx.tp
@@ -241,6 +241,7 @@ METRIC_MAPPING{{name_suffix}} = {
     'jaccard': JaccardDistance{{name_suffix}},
     'dice': DiceDistance{{name_suffix}},
     'kulsinski': KulsinskiDistance{{name_suffix}},
+    'precomputed': PrecomputedDistanceMatrix{{name_suffix}},
     'rogerstanimoto': RogersTanimotoDistance{{name_suffix}},
     'russellrao': RussellRaoDistance{{name_suffix}},
     'sokalmichener': SokalMichenerDistance{{name_suffix}},
@@ -348,6 +349,18 @@ cdef class DistanceMetric{{name_suffix}}(DistanceMetric):
     "sokalsneath"      SokalSneathDistance      NNEQ / (NNEQ + 0.5 * NTT)
     =================  =======================  ===============================
 
+    **Metrics with precomputed distances:** Any user can compute a distance
+    matrix and provide access to the distances, neighbors and other
+    data defined in this interface. The precomputed distance matrix should be
+    (n_samples_X, n_samples_Y) shape fulfilling the properties of a valid distance
+    metric.
+    
+    =================  =========================  ===============================
+    identifier         class name                 distance function
+    -----------------  -------------------------  -------------------------------
+    "precomputed"      PrecomputedDistanceMatrix  predefined
+    =================  =========================  ===============================
+
     **User-defined distance:**
 
     ===========    ===============    =======
diff --git a/sklearn/metrics/_pairwise_distances_reduction/_datasets_pair.pxd.tp b/sklearn/metrics/_pairwise_distances_reduction/_datasets_pair.pxd.tp
index 1e57b3291a8f4..fe91bf088a8c5 100644
--- a/sklearn/metrics/_pairwise_distances_reduction/_datasets_pair.pxd.tp
+++ b/sklearn/metrics/_pairwise_distances_reduction/_datasets_pair.pxd.tp
@@ -29,6 +29,11 @@ cdef class DatasetsPair{{name_suffix}}:
     cdef float64_t surrogate_dist(self, intp_t i, intp_t j) noexcept nogil
 
 
+cdef class PrecomputedDistanceMatrix{{name_suffix}}(DatasetsPair{{name_suffix}}):
+    cdef:
+        const {{INPUT_DTYPE_t}}[:, ::1] distance_matrix
+
+
 cdef class DenseDenseDatasetsPair{{name_suffix}}(DatasetsPair{{name_suffix}}):
     cdef:
         const {{INPUT_DTYPE_t}}[:, ::1] X
diff --git a/sklearn/metrics/_pairwise_distances_reduction/_datasets_pair.pyx.tp b/sklearn/metrics/_pairwise_distances_reduction/_datasets_pair.pyx.tp
index 2c3ca44047145..d0506428c1a8d 100644
--- a/sklearn/metrics/_pairwise_distances_reduction/_datasets_pair.pyx.tp
+++ b/sklearn/metrics/_pairwise_distances_reduction/_datasets_pair.pyx.tp
@@ -98,6 +98,12 @@ cdef class DatasetsPair{{name_suffix}}:
             metric_kwargs = copy.copy(metric_kwargs)
             metric_kwargs.pop("X_norm_squared", None)
             metric_kwargs.pop("Y_norm_squared", None)
+
+        if metric == 'precomputed':
+            return PrecomputedDistanceMatrix{{name_suffix}}(
+                distance_matrix=Y,
+            )
+
         cdef:
             {{DistanceMetric}} distance_metric = DistanceMetric.get_metric(
                 metric,
@@ -158,6 +164,47 @@ cdef class DatasetsPair{{name_suffix}}:
         # TODO: add "with gil: raise" here when supporting Cython 3.0
         return -1
 
+
+@final
+cdef class PrecomputedDistanceMatrix{{name_suffix}}(DatasetsPair{{name_suffix}}):
+    """A precomputed distance matrix between row vectors of two arrays.
+
+    Parameters
+    ----------
+    distance_matrix: ndarray of shape (n_samples_X, n_samples_Y)
+        Rows represent vectors. Must be C-contiguous.
+    """
+
+    def __init__(
+        self,
+        const {{INPUT_DTYPE_t}}[:, ::1] distance_matrix,
+    ):
+        super().__init__(
+            # This DistanceMetric is necessary for conversion between
+            # reduced distance and distance (it performs no-ops).
+            distance_metric={{DistanceMetric}}(),
+            n_features=0,
+        )
+        # Arrays have already been checked
+        self.distance_matrix = distance_matrix
+
+    @final
+    cdef ITYPE_t n_samples_X(self) noexcept nogil:
+        return self.distance_matrix.shape[0]
+
+    @final
+    cdef ITYPE_t n_samples_Y(self) noexcept nogil:
+        return self.distance_matrix.shape[1]
+
+    @final
+    cdef DTYPE_t surrogate_dist(self, ITYPE_t i, ITYPE_t j) noexcept nogil:
+        return self.distance_matrix[i, j]
+
+    @final
+    cdef DTYPE_t dist(self, ITYPE_t i, ITYPE_t j) noexcept nogil:
+        return self.distance_matrix[i, j]
+
+
 @final
 cdef class DenseDenseDatasetsPair{{name_suffix}}(DatasetsPair{{name_suffix}}):
     """Compute distances between row vectors of two arrays.
diff --git a/sklearn/metrics/_pairwise_distances_reduction/_dispatcher.py b/sklearn/metrics/_pairwise_distances_reduction/_dispatcher.py
index 956de3577bcee..501ba58416d17 100644
--- a/sklearn/metrics/_pairwise_distances_reduction/_dispatcher.py
+++ b/sklearn/metrics/_pairwise_distances_reduction/_dispatcher.py
@@ -78,7 +78,7 @@ def valid_metrics(cls) -> List[str]:
             "hamming",
             *BOOL_METRICS,
         }
-        return sorted(({"sqeuclidean"} | set(METRIC_MAPPING64.keys())) - excluded)
+        return sorted(({"sqeuclidean", "precomputed"} | set(METRIC_MAPPING64.keys())) - excluded)
 
     @classmethod
     def is_usable_for(cls, X, Y, metric) -> bool: