diff --git a/sklearn/cluster/_dbscan.py b/sklearn/cluster/_dbscan.py
index 857a332cc2371..8d6d609811458 100644
--- a/sklearn/cluster/_dbscan.py
+++ b/sklearn/cluster/_dbscan.py
@@ -5,7 +5,6 @@
 # Authors: The scikit-learn developers
 # SPDX-License-Identifier: BSD-3-Clause
 
-import warnings
 from numbers import Integral, Real
 
 import numpy as np
@@ -399,14 +398,6 @@ def fit(self, X, y=None, sample_weight=None):
         # Calculate neighborhood for all samples. This leaves the original
         # point in, which needs to be considered later (i.e. point i is in the
         # neighborhood of point i. While True, its useless information)
-        if self.metric == "precomputed" and sparse.issparse(X):
-            # set the diagonal to explicit values, as a point is its own
-            # neighbor
-            X = X.copy()  # copy to avoid in-place modification
-            with warnings.catch_warnings():
-                warnings.simplefilter("ignore", sparse.SparseEfficiencyWarning)
-                X.setdiag(X.diagonal())
-
         neighbors_model = NearestNeighbors(
             radius=self.eps,
             algorithm=self.algorithm,
@@ -420,6 +411,13 @@ def fit(self, X, y=None, sample_weight=None):
         # This has worst case O(n^2) memory complexity
         neighborhoods = neighbors_model.radius_neighbors(X, return_distance=False)
 
+        # Each point is its own neighbor, so update the neighborhoods
+        # accordingly after the initial fitting
+        if self.metric == "precomputed" and sparse.issparse(X):
+            for i, neighborhood in enumerate(neighborhoods):
+                if i not in neighborhoods[i]:
+                    neighborhoods[i] = np.append(neighborhood, i)
+
         if sample_weight is None:
             n_neighbors = np.array([len(neighbors) for neighbors in neighborhoods])
         else: