diff --git a/promql/functions.go b/promql/functions.go
index 027c4495ab8..ecd6f7c8b4e 100644
--- a/promql/functions.go
+++ b/promql/functions.go
@@ -88,7 +88,7 @@ func extrapolatedRate(vals []parser.Value, args parser.Expressions, enh *EvalNod
 		return enh.Out, annos.Add(annotations.NewMixedFloatsHistogramsWarning(metricName, args[0].PositionRange()))
 	}
 
-	if isCounter &&
+	if isCounter && metricName != "" && len(samples.Floats) > 0 &&
 		!strings.HasSuffix(metricName, "_total") &&
 		!strings.HasSuffix(metricName, "_sum") &&
 		!strings.HasSuffix(metricName, "_count") &&
diff --git a/util/annotations/annotations.go b/util/annotations/annotations.go
index 8bdcc65bad9..9cfbb121f6c 100644
--- a/util/annotations/annotations.go
+++ b/util/annotations/annotations.go
@@ -156,8 +156,8 @@ func NewMixedClassicNativeHistogramsWarning(metricName string, pos posrange.Posi
 	}
 }
 
-// NewPossibleNonCounterInfo is used when a counter metric does not have the suffixes
-// _total, _sum, _count, or _bucket.
+// NewPossibleNonCounterInfo is used when a named counter metric with only float samples does not
+// have the suffixes _total, _sum, _count, or _bucket.
 func NewPossibleNonCounterInfo(metricName string, pos posrange.PositionRange) annoErr {
 	return annoErr{
 		PositionRange: pos,