diff --git a/app/vmagent/influx/request_handler.go b/app/vmagent/influx/request_handler.go
index b39d365f3..9da1be933 100644
--- a/app/vmagent/influx/request_handler.go
+++ b/app/vmagent/influx/request_handler.go
@@ -96,7 +96,8 @@ func insertRows(db string, rows []parser.Row, extraLabels []prompbmarshal.Label)
 		if !*skipMeasurement {
 			ctx.metricGroupBuf = append(ctx.metricGroupBuf, r.Measurement...)
 		}
-		skipFieldKey := len(r.Fields) == 1 && *skipSingleField
+		// See https://github.com/VictoriaMetrics/VictoriaMetrics/issues/1139
+		skipFieldKey := len(r.Measurement) > 0 && len(r.Fields) == 1 && *skipSingleField
 		if len(ctx.metricGroupBuf) > 0 && !skipFieldKey {
 			ctx.metricGroupBuf = append(ctx.metricGroupBuf, *measurementFieldSeparator...)
 		}
diff --git a/app/vminsert/influx/request_handler.go b/app/vminsert/influx/request_handler.go
index 4e4e17c28..784c2c3ec 100644
--- a/app/vminsert/influx/request_handler.go
+++ b/app/vminsert/influx/request_handler.go
@@ -96,7 +96,8 @@ func insertRows(db string, rows []parser.Row, extraLabels []prompbmarshal.Label)
 		if !*skipMeasurement {
 			ctx.metricGroupBuf = append(ctx.metricGroupBuf, r.Measurement...)
 		}
-		skipFieldKey := len(r.Fields) == 1 && *skipSingleField
+		// See https://github.com/VictoriaMetrics/VictoriaMetrics/issues/1139
+		skipFieldKey := len(r.Measurement) > 0 && len(r.Fields) == 1 && *skipSingleField
 		if len(ctx.metricGroupBuf) > 0 && !skipFieldKey {
 			ctx.metricGroupBuf = append(ctx.metricGroupBuf, *measurementFieldSeparator...)
 		}