diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index da2a9bdada469..2b437734a451a 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -673,6 +673,7 @@ Timezones
 
 Numeric
 ^^^^^^^
+- Bug in :meth:`DataFrame.corr` where numerical precision errors resulted in correlations above ``1.0`` (:issue:`61120`)
 - Bug in :meth:`DataFrame.quantile` where the column type was not preserved when ``numeric_only=True`` with a list-like ``q`` produced an empty result (:issue:`59035`)
 - Bug in ``np.matmul`` with :class:`Index` inputs raising a ``TypeError`` (:issue:`57079`)
 
diff --git a/pandas/_libs/algos.pyx b/pandas/_libs/algos.pyx
index 60ee73ef6b43f..9dfa4a9486558 100644
--- a/pandas/_libs/algos.pyx
+++ b/pandas/_libs/algos.pyx
@@ -353,10 +353,9 @@ def nancorr(const float64_t[:, :] mat, bint cov=False, minp=None):
         float64_t[:, ::1] result
         uint8_t[:, :] mask
         int64_t nobs = 0
-        float64_t vx, vy, dx, dy, meanx, meany, divisor, ssqdmx, ssqdmy, covxy
+        float64_t vx, vy, dx, dy, meanx, meany, divisor, ssqdmx, ssqdmy, covxy, val
 
     N, K = (<object>mat).shape
-
     if minp is None:
         minpv = 1
     else:
@@ -389,8 +388,14 @@ def nancorr(const float64_t[:, :] mat, bint cov=False, minp=None):
                 else:
                     divisor = (nobs - 1.0) if cov else sqrt(ssqdmx * ssqdmy)
 
+                    # clip `covxy / divisor` to ensure coeff is within bounds
                     if divisor != 0:
-                        result[xi, yi] = result[yi, xi] = covxy / divisor
+                        val = covxy / divisor
+                        if val > 1.0:
+                            val = 1.0
+                        elif val < -1.0:
+                            val = -1.0
+                        result[xi, yi] = result[yi, xi] = val
                     else:
                         result[xi, yi] = result[yi, xi] = NaN
 
diff --git a/pandas/tests/frame/methods/test_cov_corr.py b/pandas/tests/frame/methods/test_cov_corr.py
index d5e94382b8314..6dfbc325aafa4 100644
--- a/pandas/tests/frame/methods/test_cov_corr.py
+++ b/pandas/tests/frame/methods/test_cov_corr.py
@@ -485,3 +485,15 @@ def test_corrwith_min_periods_boolean(self):
         result = df_bool.corrwith(ser_bool, min_periods=3)
         expected = Series([0.57735, 0.57735], index=["A", "B"])
         tm.assert_series_equal(result, expected)
+
+    def test_corr_within_bounds(self):
+        df1 = DataFrame({"x": [0, 1], "y": [1.35951, 1.3595100000000007]})
+        result1 = df1.corr().max().max()
+        expected1 = 1.0
+        tm.assert_equal(result1, expected1)
+
+        rng = np.random.default_rng(seed=42)
+        df2 = DataFrame(rng.random((100, 4)))
+        corr_matrix = df2.corr()
+        assert corr_matrix.min().min() >= -1.0
+        assert corr_matrix.max().max() <= 1.0