diff --git a/libcontainer/container_linux.go b/libcontainer/container_linux.go
index 8abdc3fe9..3dca29e4c 100644
--- a/libcontainer/container_linux.go
+++ b/libcontainer/container_linux.go
@@ -2067,9 +2067,20 @@ func ignoreTerminateErrors(err error) error {
 	if err == nil {
 		return nil
 	}
+	// terminate() might return an error from ether Kill or Wait.
+	// The (*Cmd).Wait documentation says: "If the command fails to run
+	// or doesn't complete successfully, the error is of type *ExitError".
+	// Filter out such errors (like "exit status 1" or "signal: killed").
+	var exitErr *exec.ExitError
+	if errors.As(err, &exitErr) {
+		return nil
+	}
+	// TODO: use errors.Is(err, os.ErrProcessDone) here and
+	// remove "process already finished" string comparison below
+	// once go 1.16 is minimally supported version.
+
 	s := err.Error()
-	if strings.Contains(s, "signal: killed") ||
-		strings.Contains(s, "process already finished") ||
+	if strings.Contains(s, "process already finished") ||
 		strings.Contains(s, "Wait was already called") {
 		return nil
 	}