diff --git a/docs/querying/functions.md b/docs/querying/functions.md
index 419823430..0698658b5 100644
--- a/docs/querying/functions.md
+++ b/docs/querying/functions.md
@@ -182,8 +182,8 @@ is assumed to be 0 if the upper bound of that bucket is greater than
 bucket. Otherwise, the upper bound of the lowest bucket is returned
 for quantiles located in the lowest bucket.
 
-If `b` contains fewer than two buckets, `NaN` is returned. For φ < 0, `-Inf` is
-returned. For φ > 1, `+Inf` is returned.
+If `b` has 0 observations, `NaN` is returned. If `b` contains fewer than two buckets,
+`NaN` is returned. For φ < 0, `-Inf` is returned. For φ > 1, `+Inf` is returned.
 
 ## `holt_winters()`
 
diff --git a/promql/quantile.go b/promql/quantile.go
index 6fef2c4f6..6e63efab6 100644
--- a/promql/quantile.go
+++ b/promql/quantile.go
@@ -61,6 +61,8 @@ type metricWithBuckets struct {
 // happening during evaluations of AST functions, we should report those
 // explicitly):
 //
+// If 'buckets' has 0 observations, NaN is returned.
+//
 // If 'buckets' has fewer than 2 elements, NaN is returned.
 //
 // If the highest bucket is not +Inf, NaN is returned.
@@ -86,8 +88,11 @@ func bucketQuantile(q float64, buckets buckets) float64 {
 	if len(buckets) < 2 {
 		return math.NaN()
 	}
-
-	rank := q * buckets[len(buckets)-1].count
+	observations := buckets[len(buckets)-1].count
+	if observations == 0 {
+		return math.NaN()
+	}
+	rank := q * observations
 	b := sort.Search(len(buckets)-1, func(i int) bool { return buckets[i].count >= rank })
 
 	if b == len(buckets)-1 {
diff --git a/promql/testdata/histograms.test b/promql/testdata/histograms.test
index 594295c56..b7ec13682 100644
--- a/promql/testdata/histograms.test
+++ b/promql/testdata/histograms.test
@@ -179,3 +179,11 @@ eval instant at 50m histogram_quantile(0.75, rate(mixed_bucket[5m]))
 eval instant at 50m histogram_quantile(1, rate(mixed_bucket[5m]))
 	{instance="ins1", job="job1"} 0.2
 	{instance="ins2", job="job1"} NaN
+
+load 5m
+	empty_bucket{le="0.1", job="job1", instance="ins1"}    0x10
+	empty_bucket{le="0.2", job="job1", instance="ins1"}    0x10
+	empty_bucket{le="+Inf", job="job1", instance="ins1"}   0x10
+
+eval instant at 50m histogram_quantile(0.2, rate(empty_bucket[5m]))
+	{instance="ins1", job="job1"} NaN
\ No newline at end of file