diff --git a/promql/functions.go b/promql/functions.go
index e0b811a09d..6853307d0e 100644
--- a/promql/functions.go
+++ b/promql/functions.go
@@ -1111,6 +1111,9 @@ func funcHistogramStdDev(vals []parser.Value, args parser.Expressions, enh *Eval
 		it := sample.H.AllBucketIterator()
 		for it.Next() {
 			bucket := it.At()
+			if bucket.Count == 0 {
+				continue
+			}
 			var val float64
 			if bucket.Lower <= 0 && 0 <= bucket.Upper {
 				val = 0
@@ -1147,6 +1150,9 @@ func funcHistogramStdVar(vals []parser.Value, args parser.Expressions, enh *Eval
 		it := sample.H.AllBucketIterator()
 		for it.Next() {
 			bucket := it.At()
+			if bucket.Count == 0 {
+				continue
+			}
 			var val float64
 			if bucket.Lower <= 0 && 0 <= bucket.Upper {
 				val = 0