diff --git a/docs/querying/functions.md b/docs/querying/functions.md
index 33740ac4ab..1de8bb2aa9 100644
--- a/docs/querying/functions.md
+++ b/docs/querying/functions.md
@@ -192,7 +192,7 @@ bucket. Otherwise, the upper bound of the lowest bucket is returned
 for quantiles located in the lowest bucket.
 
 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.
+`NaN` is returned. For φ < 0, `-Inf` is returned. For φ > 1, `+Inf` is returned. For φ = `NaN`, `NaN` is returned.
 
 ## `holt_winters()`
 
@@ -456,4 +456,4 @@ The following are useful for converting between degrees and radians:
 
 - `deg(v instant-vector)`: converts radians to degrees for all elements in `v`.
 - `pi()`: returns pi.
-- `rad(v instant-vector)`: converts degrees to radians for all elements in `v`.
\ No newline at end of file
+- `rad(v instant-vector)`: converts degrees to radians for all elements in `v`.
diff --git a/docs/querying/operators.md b/docs/querying/operators.md
index a0491bdbeb..9f35e0c153 100644
--- a/docs/querying/operators.md
+++ b/docs/querying/operators.md
@@ -241,7 +241,7 @@ vector. `by` and `without` are only used to bucket the input vector.
 `quantile` calculates the φ-quantile, the value that ranks at number φ*N among
 the N metric values of the dimensions aggregated over. φ is provided as the
 aggregation parameter. For example, `quantile(0.5, ...)` calculates the median,
-`quantile(0.95, ...)` the 95th percentile.
+`quantile(0.95, ...)` the 95th percentile. For φ = `NaN`, `NaN` is returned. For φ < 0, `-Inf` is returned. For φ > 1, `+Inf` is returned.
 
 Example:
 
diff --git a/promql/quantile.go b/promql/quantile.go
index e2de98840c..a3abf68dd0 100644
--- a/promql/quantile.go
+++ b/promql/quantile.go
@@ -67,10 +67,15 @@ type metricWithBuckets struct {
 //
 // If the highest bucket is not +Inf, NaN is returned.
 //
+// If q==NaN, NaN is returned.
+//
 // If q<0, -Inf is returned.
 //
 // If q>1, +Inf is returned.
 func bucketQuantile(q float64, buckets buckets) float64 {
+	if math.IsNaN(q) {
+		return math.NaN()
+	}
 	if q < 0 {
 		return math.Inf(-1)
 	}
@@ -182,10 +187,11 @@ func ensureMonotonic(buckets buckets) {
 //
 // The Vector will be sorted.
 // If 'values' has zero elements, NaN is returned.
+// If q==NaN, NaN is returned.
 // If q<0, -Inf is returned.
 // If q>1, +Inf is returned.
 func quantile(q float64, values vectorByValueHeap) float64 {
-	if len(values) == 0 {
+	if len(values) == 0 || math.IsNaN(q) {
 		return math.NaN()
 	}
 	if q < 0 {
diff --git a/promql/testdata/aggregators.test b/promql/testdata/aggregators.test
index 220c5edce1..8709b393b2 100644
--- a/promql/testdata/aggregators.test
+++ b/promql/testdata/aggregators.test
@@ -399,6 +399,11 @@ eval instant at 1m quantile without(point)((scalar(foo)), data)
 	{test="three samples"} 1.6
 	{test="uneven samples"} 2.8
 
+eval instant at 1m quantile without(point)(NaN, data)
+    {test="two samples"} NaN
+    {test="three samples"} NaN
+    {test="uneven samples"} NaN
+
 # Tests for group.
 clear
 
diff --git a/promql/testdata/histograms.test b/promql/testdata/histograms.test
index 508f1eface..f30c07e7b3 100644
--- a/promql/testdata/histograms.test
+++ b/promql/testdata/histograms.test
@@ -60,6 +60,11 @@ eval instant at 50m histogram_quantile(1.01, testhistogram_bucket)
 	{start="positive"} +Inf
 	{start="negative"} +Inf
 
+# Quantile invalid.
+eval instant at 50m histogram_quantile(NaN, testhistogram_bucket)
+	{start="positive"} NaN
+	{start="negative"} NaN
+
 # Quantile value in lowest bucket, which is positive.
 eval instant at 50m histogram_quantile(0, testhistogram_bucket{start="positive"})
 	{start="positive"} 0