diff --git a/doc/whats_new/v1.2.rst b/doc/whats_new/v1.2.rst
index 75ce01b54f3a7..80010afc30516 100644
--- a/doc/whats_new/v1.2.rst
+++ b/doc/whats_new/v1.2.rst
@@ -243,6 +243,11 @@ Changelog
   `nu=0.5` for PyPy (and possibly other non CPython interpreters). :pr:`24245`
   by :user:`Loïc Estève <lesteve>`.
 
+- |Fix| The `fit` method of :class:`gaussian_process.GaussianProcessRegressor`
+  will not modify the input X in case a custom kernel is used, with a `diag`
+  method that returns part of the input X. :pr:`24405`
+  by :user:`Omar Salman <OmarManzoor>`.
+
 :mod:`sklearn.kernel_approximation`
 ...................................
 
@@ -305,7 +310,7 @@ Changelog
 - |Fix| Allows `csr_matrix` as input for parameter: `y_true` of
    the :func:`metrics.label_ranking_average_precision_score` metric.
    :pr:`23442` by :user:`Sean Atukorala <ShehanAT>`
-  
+
 - |Fix| :func:`metrics.ndcg_score` will now trigger a warning when the `y_true`
   value contains a negative value. Users may still use negative values, but the
   result may not be between 0 and 1. Starting in v1.4, passing in negative
diff --git a/sklearn/gaussian_process/_gpr.py b/sklearn/gaussian_process/_gpr.py
index 4777d0d80627c..c0a8dc71b7352 100644
--- a/sklearn/gaussian_process/_gpr.py
+++ b/sklearn/gaussian_process/_gpr.py
@@ -435,7 +435,7 @@ def predict(self, X, return_std=False, return_cov=False):
                 # Compute variance of predictive distribution
                 # Use einsum to avoid explicitly forming the large matrix
                 # V^T @ V just to extract its diagonal afterward.
-                y_var = self.kernel_.diag(X)
+                y_var = self.kernel_.diag(X).copy()
                 y_var -= np.einsum("ij,ji->i", V.T, V)
 
                 # Check if any of the variances is negative because of
diff --git a/sklearn/gaussian_process/tests/test_gpr.py b/sklearn/gaussian_process/tests/test_gpr.py
index 784aa88d6487c..c03778958a3ad 100644
--- a/sklearn/gaussian_process/tests/test_gpr.py
+++ b/sklearn/gaussian_process/tests/test_gpr.py
@@ -14,7 +14,11 @@
 import pytest
 
 from sklearn.gaussian_process import GaussianProcessRegressor
-from sklearn.gaussian_process.kernels import RBF, ConstantKernel as C, WhiteKernel
+from sklearn.gaussian_process.kernels import (
+    RBF,
+    ConstantKernel as C,
+    WhiteKernel,
+)
 from sklearn.gaussian_process.kernels import DotProduct, ExpSineSquared
 from sklearn.gaussian_process.tests._mini_sequence_kernel import MiniSeqKernel
 from sklearn.exceptions import ConvergenceWarning
@@ -767,3 +771,30 @@ def test_sample_y_shapes(normalize_y, n_targets):
 
     y_samples = model.sample_y(X_test, n_samples=n_samples_y_test)
     assert y_samples.shape == y_test_shape
+
+
+class CustomKernel(C):
+    """
+    A custom kernel that has a diag method that returns the first column of the
+    input matrix X. This is a helper for the test to check that the input
+    matrix X is not mutated.
+    """
+
+    def diag(self, X):
+        return X[:, 0]
+
+
+def test_gpr_predict_input_not_modified():
+    """
+    Check that the input X is not modified by the predict method of the
+    GaussianProcessRegressor when setting return_std=True.
+
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/24340
+    """
+    gpr = GaussianProcessRegressor(kernel=CustomKernel()).fit(X, y)
+
+    X2_copy = np.copy(X2)
+    _, _ = gpr.predict(X2, return_std=True)
+
+    assert_allclose(X2, X2_copy)