diff --git a/src/cmd/go/internal/modcmd/tidy.go b/src/cmd/go/internal/modcmd/tidy.go
index 789e936608..8c68ec51d8 100644
--- a/src/cmd/go/internal/modcmd/tidy.go
+++ b/src/cmd/go/internal/modcmd/tidy.go
@@ -64,6 +64,7 @@ func runTidy(cmd *base.Command, args []string) {
 		}
 	}
 	modload.SetBuildList(keep)
+	modload.AddGoStmt()
 	modTidyGoSum() // updates memory copy; WriteGoMod on next line flushes it out
 	modload.WriteGoMod()
 }
diff --git a/src/cmd/go/internal/modload/init.go b/src/cmd/go/internal/modload/init.go
index 4bc4a2449c..fad204a2dd 100644
--- a/src/cmd/go/internal/modload/init.go
+++ b/src/cmd/go/internal/modload/init.go
@@ -408,10 +408,9 @@ func legacyModInit() {
 		fmt.Fprintf(os.Stderr, "go: creating new go.mod: module %s\n", path)
 		modFile = new(modfile.File)
 		modFile.AddModuleStmt(path)
+		AddGoStmt()
 	}
 
-	addGoStmt()
-
 	for _, name := range altConfigs {
 		cfg := filepath.Join(modRoot, name)
 		data, err := ioutil.ReadFile(cfg)
@@ -420,6 +419,7 @@ func legacyModInit() {
 			if convert == nil {
 				return
 			}
+			AddGoStmt()
 			fmt.Fprintf(os.Stderr, "go: copying requirements from %s\n", base.ShortPath(cfg))
 			cfg = filepath.ToSlash(cfg)
 			if err := modconv.ConvertLegacyConfig(modFile, cfg, data); err != nil {
@@ -434,8 +434,12 @@ func legacyModInit() {
 	}
 }
 
-// addGoStmt adds a go statement referring to the current version.
-func addGoStmt() {
+// AddGoStmt adds a go directive to the go.mod file if it does not already include one.
+// The 'go' version added, if any, is the latest version supported by this toolchain.
+func AddGoStmt() {
+	if modFile.Go != nil && modFile.Go.Version != "" {
+		return
+	}
 	tags := build.Default.ReleaseTags
 	version := tags[len(tags)-1]
 	if !strings.HasPrefix(version, "go") || !modfile.GoVersionRE.MatchString(version[2:]) {
diff --git a/src/cmd/go/testdata/script/mod_init_empty.txt b/src/cmd/go/testdata/script/mod_init_empty.txt
new file mode 100644
index 0000000000..b6357bb053
--- /dev/null
+++ b/src/cmd/go/testdata/script/mod_init_empty.txt
@@ -0,0 +1,16 @@
+env GO111MODULE=on
+
+env GOPATH=$devnull
+
+go list -m
+stdout '^example.com$'
+
+go list
+stdout '^example.com$'
+
+-- go.mod --
+module example.com
+-- main.go --
+package main
+
+func main() {}
diff --git a/src/cmd/go/testdata/script/mod_std_vendor.txt b/src/cmd/go/testdata/script/mod_std_vendor.txt
index 5aa544cb77..5986cff594 100644
--- a/src/cmd/go/testdata/script/mod_std_vendor.txt
+++ b/src/cmd/go/testdata/script/mod_std_vendor.txt
@@ -20,7 +20,7 @@ stdout ^vendor/golang.org/x/crypto # dep of .TestImports
 # Modules outside the standard library should not use the packages vendored there...
 cd broken
 ! go build -mod=readonly
-stderr 'updates to go.mod needed'
+stderr 'disabled by -mod=readonly'
 ! go build -mod=vendor
 stderr 'cannot find package'
 stderr 'hpack'