diff --git a/storage/remote/codec.go b/storage/remote/codec.go
index fa033b589..fb4d777a3 100644
--- a/storage/remote/codec.go
+++ b/storage/remote/codec.go
@@ -360,6 +360,9 @@ func (c *concreteSeriesIterator) Seek(t int64) bool {
 	if c.cur == -1 {
 		c.cur = 0
 	}
+	if c.cur >= len(c.series.samples) {
+		return false
+	}
 	// No-op check.
 	if s := c.series.samples[c.cur]; s.Timestamp >= t {
 		return true
diff --git a/storage/remote/codec_test.go b/storage/remote/codec_test.go
index 1432736e1..be52bd312 100644
--- a/storage/remote/codec_test.go
+++ b/storage/remote/codec_test.go
@@ -233,6 +233,11 @@ func TestConcreteSeriesIterator(t *testing.T) {
 	ts, v = it.At()
 	require.Equal(t, int64(3), ts)
 	require.Equal(t, 3., v)
+
+	// Seek beyond the end.
+	require.False(t, it.Seek(5))
+	// And we don't go back. (This exposes issue #10027.)
+	require.False(t, it.Seek(2))
 }
 
 func TestFromQueryResultWithDuplicates(t *testing.T) {
diff --git a/storage/series.go b/storage/series.go
index 024b0fc72..2dba83715 100644
--- a/storage/series.go
+++ b/storage/series.go
@@ -99,6 +99,9 @@ func (it *listSeriesIterator) Seek(t int64) bool {
 	if it.idx == -1 {
 		it.idx = 0
 	}
+	if it.idx >= it.samples.Len() {
+		return false
+	}
 	// No-op check.
 	if s := it.samples.Get(it.idx); s.T() >= t {
 		return true
diff --git a/storage/series_test.go b/storage/series_test.go
index 384009de4..8ce4a7222 100644
--- a/storage/series_test.go
+++ b/storage/series_test.go
@@ -51,4 +51,9 @@ func TestListSeriesIterator(t *testing.T) {
 	ts, v = it.At()
 	require.Equal(t, int64(3), ts)
 	require.Equal(t, 3., v)
+
+	// Seek beyond the end.
+	require.False(t, it.Seek(5))
+	// And we don't go back. (This exposes issue #10027.)
+	require.False(t, it.Seek(2))
 }
diff --git a/tsdb/tsdbutil/buffer_test.go b/tsdb/tsdbutil/buffer_test.go
index baae8266b..f19403360 100644
--- a/tsdb/tsdbutil/buffer_test.go
+++ b/tsdb/tsdbutil/buffer_test.go
@@ -159,6 +159,9 @@ func (it *listSeriesIterator) Seek(t int64) bool {
 	if it.idx == -1 {
 		it.idx = 0
 	}
+	if it.idx >= len(it.list) {
+		return false
+	}
 	// No-op check.
 	if s := it.list[it.idx]; s.T() >= t {
 		return true