diff --git a/src/cmd/go/internal/modload/mvs.go b/src/cmd/go/internal/modload/mvs.go
index 94373bc5f3..045cbead3b 100644
--- a/src/cmd/go/internal/modload/mvs.go
+++ b/src/cmd/go/internal/modload/mvs.go
@@ -58,7 +58,7 @@ func (r *mvsReqs) Required(mod module.Version) ([]module.Version, error) {
 // be chosen over other versions of the same module in the module dependency
 // graph.
 func (*mvsReqs) Max(v1, v2 string) string {
-	if v1 != "" && semver.Compare(v1, v2) == -1 {
+	if v1 != "" && (v2 == "" || semver.Compare(v1, v2) == -1) {
 		return v2
 	}
 	return v1
diff --git a/src/cmd/go/internal/modload/mvs_test.go b/src/cmd/go/internal/modload/mvs_test.go
new file mode 100644
index 0000000000..0cb376ec3c
--- /dev/null
+++ b/src/cmd/go/internal/modload/mvs_test.go
@@ -0,0 +1,33 @@
+// Copyright 2020 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package modload_test
+
+import (
+	"testing"
+
+	"cmd/go/internal/modload"
+)
+
+func TestReqsMax(t *testing.T) {
+	type testCase struct {
+		a, b, want string
+	}
+	reqs := modload.Reqs()
+	for _, tc := range []testCase{
+		{a: "v0.1.0", b: "v0.2.0", want: "v0.2.0"},
+		{a: "v0.2.0", b: "v0.1.0", want: "v0.2.0"},
+		{a: "", b: "v0.1.0", want: ""}, // "" is Target.Version
+		{a: "v0.1.0", b: "", want: ""},
+		{a: "none", b: "v0.1.0", want: "v0.1.0"},
+		{a: "v0.1.0", b: "none", want: "v0.1.0"},
+		{a: "none", b: "", want: ""},
+		{a: "", b: "none", want: ""},
+	} {
+		max := reqs.Max(tc.a, tc.b)
+		if max != tc.want {
+			t.Errorf("Reqs().Max(%q, %q) = %q; want %q", tc.a, tc.b, max, tc.want)
+		}
+	}
+}