diff --git a/libs/exponential-histogram/src/main/java/org/elasticsearch/exponentialhistogram/ExponentialHistogramQuantile.java b/libs/exponential-histogram/src/main/java/org/elasticsearch/exponentialhistogram/ExponentialHistogramQuantile.java
index 218873982b1b3..bcac4bfb0907f 100644
--- a/libs/exponential-histogram/src/main/java/org/elasticsearch/exponentialhistogram/ExponentialHistogramQuantile.java
+++ b/libs/exponential-histogram/src/main/java/org/elasticsearch/exponentialhistogram/ExponentialHistogramQuantile.java
@@ -34,6 +34,7 @@ public class ExponentialHistogramQuantile {
      * It returns the value of the element at rank {@code max(0, min(n - 1, (quantile * (n + 1)) - 1))}, where n is the total number of
      * values and rank starts at 0. If the rank is fractional, the result is linearly interpolated from the values of the two
      * neighboring ranks.
+     * The result is clamped to the histogram's minimum and maximum values.
      *
      * @param histo    the histogram representing the distribution
      * @param quantile the quantile to query, in the range [0, 1]
@@ -60,6 +61,8 @@ public static double getQuantile(ExponentialHistogram histo, double quantile) {
         double upperFactor = exactRank - lowerRank;
 
         ValueAndPreviousValue values = getElementAtRank(histo, upperRank);
+        // Ensure we don't return values outside the histogram's range
+        values = values.clampTo(histo.min(), histo.max());
 
         double result;
         if (lowerRank == upperRank) {
@@ -158,8 +161,13 @@ private static ValueAndPreviousValue getBucketMidpointForRank(BucketIterator buc
      * @param valueAtRank         the value at the desired rank
      */
     private record ValueAndPreviousValue(double valueAtPreviousRank, double valueAtRank) {
+
         ValueAndPreviousValue negateAndSwap() {
             return new ValueAndPreviousValue(-valueAtRank, -valueAtPreviousRank);
         }
+
+        ValueAndPreviousValue clampTo(double min, double max) {
+            return new ValueAndPreviousValue(Math.clamp(valueAtPreviousRank, min, max), Math.clamp(valueAtRank, min, max));
+        }
     }
 }
diff --git a/libs/exponential-histogram/src/test/java/org/elasticsearch/exponentialhistogram/QuantileAccuracyTests.java b/libs/exponential-histogram/src/test/java/org/elasticsearch/exponentialhistogram/QuantileAccuracyTests.java
index 141a9fd5b1fb0..2991fd96e6b3d 100644
--- a/libs/exponential-histogram/src/test/java/org/elasticsearch/exponentialhistogram/QuantileAccuracyTests.java
+++ b/libs/exponential-histogram/src/test/java/org/elasticsearch/exponentialhistogram/QuantileAccuracyTests.java
@@ -63,6 +63,44 @@ public void testNoNegativeZeroReturned() {
         assertThat(median, equalTo(0.0));
     }
 
+    public void testPercentilesClampedToMinMax() {
+        ExponentialHistogram histogram = createAutoReleasedHistogram(
+            b -> b.scale(0).setNegativeBucket(1, 1).setPositiveBucket(1, 1).max(0.00001).min(-0.00002)
+        );
+        double p0 = ExponentialHistogramQuantile.getQuantile(histogram, 0.0);
+        double p100 = ExponentialHistogramQuantile.getQuantile(histogram, 1.0);
+        assertThat(p0, equalTo(-0.00002));
+        assertThat(p100, equalTo(0.00001));
+    }
+
+    public void testMinMaxClampedPercentileAccuracy() {
+        ExponentialHistogram histogram = createAutoReleasedHistogram(
+            b -> b.scale(0)
+                .setPositiveBucket(0, 1) // bucket 0 covers (1, 2]
+                .setPositiveBucket(1, 1) // bucket 1 covers (2, 4]
+                .min(1.1)
+                .max(2.1)
+        );
+
+        // The 0.5 percentile linearly interpolates between the two buckets.
+        // For the (1, 2] bucket, the point of least relative error will be used (1.33333)
+        // For the (2, 4] bucket, the max of the histogram should be used instead (2.1)
+        double expectedResult = (4.0 / 3 + 2.1) / 2;
+        double p50 = ExponentialHistogramQuantile.getQuantile(histogram, 0.5);
+        assertThat(p50, equalTo(expectedResult));
+
+        // Test the same for min instead of max
+        histogram = createAutoReleasedHistogram(
+            b -> b.scale(0)
+                .setNegativeBucket(0, 1) // bucket 0 covers (1, 2]
+                .setNegativeBucket(1, 1) // bucket 1 covers (2, 4]
+                .min(-2.1)
+                .max(-1.1)
+        );
+        p50 = ExponentialHistogramQuantile.getQuantile(histogram, 0.5);
+        assertThat(p50, equalTo(-expectedResult));
+    }
+
     public void testUniformDistribution() {
         testDistributionQuantileAccuracy(new UniformRealDistribution(new Well19937c(randomInt()), 0, 100));
     }