diff --git a/tsdb/tsm1/file_store.go b/tsdb/tsm1/file_store.go
index 8934949731..0052c5b058 100644
--- a/tsdb/tsm1/file_store.go
+++ b/tsdb/tsm1/file_store.go
@@ -745,6 +745,14 @@ func (f *FileStore) replace(oldFiles, newFiles []string, updatedFn func(r []TSMF
 			return err
 		}
 
+		// Observe the associated statistics file, if available.
+		statsFile := StatsFilename(file)
+		if _, err := os.Stat(statsFile); err == nil {
+			if err := f.obs.FileFinishing(statsFile); err != nil {
+				return err
+			}
+		}
+
 		var newName = file
 		if strings.HasSuffix(file, tsmTmpExt) {
 			// The new TSM files have a tmp extension.  First rename them.
@@ -802,6 +810,14 @@ func (f *FileStore) replace(oldFiles, newFiles []string, updatedFn func(r []TSMF
 					return err
 				}
 
+				// Remove associated stats file.
+				statsFile := StatsFilename(file.Path())
+				if _, err := os.Stat(statsFile); err == nil {
+					if err := f.obs.FileUnlinking(statsFile); err != nil {
+						return err
+					}
+				}
+
 				for _, t := range file.TombstoneFiles() {
 					if err := f.obs.FileUnlinking(t.Path); err != nil {
 						return err