diff --git a/git/git.go b/git/git.go
index 3cda262f0..53e7089da 100644
--- a/git/git.go
+++ b/git/git.go
@@ -308,8 +308,13 @@ func RunClone(cloneURL string, args []string) (target string, err error) {
 	return
 }
 
-func AddUpstreamRemote(upstreamURL, cloneDir string) error {
-	cloneCmd, err := GitCommand("-C", cloneDir, "remote", "add", "-f", "upstream", upstreamURL)
+func AddUpstreamRemote(upstreamURL, cloneDir string, branches []string) error {
+	args := []string{"-C", cloneDir, "remote", "add"}
+	for _, branch := range branches {
+		args = append(args, "-t", branch)
+	}
+	args = append(args, "-f", "upstream", upstreamURL)
+	cloneCmd, err := GitCommand(args...)
 	if err != nil {
 		return err
 	}
diff --git a/git/git_test.go b/git/git_test.go
index 34cc9c7cb..a432f74b5 100644
--- a/git/git_test.go
+++ b/git/git_test.go
@@ -3,10 +3,12 @@ package git
 import (
 	"os/exec"
 	"reflect"
+	"strings"
 	"testing"
 
 	"github.com/cli/cli/internal/run"
 	"github.com/cli/cli/test"
+	"github.com/stretchr/testify/assert"
 )
 
 func Test_UncommittedChangeCount(t *testing.T) {
@@ -170,5 +172,45 @@ func TestParseExtraCloneArgs(t *testing.T) {
 			}
 		})
 	}
-
+}
+
+func TestAddUpstreamRemote(t *testing.T) {
+	tests := []struct {
+		name        string
+		upstreamURL string
+		cloneDir    string
+		branches    []string
+		want        string
+	}{
+		{
+			name:        "fetch all",
+			upstreamURL: "URL",
+			cloneDir:    "DIRECTORY",
+			branches:    []string{},
+			want:        "git -C DIRECTORY remote add -f upstream URL",
+		},
+		{
+			name:        "fetch specific branches only",
+			upstreamURL: "URL",
+			cloneDir:    "DIRECTORY",
+			branches:    []string{"master", "dev"},
+			want:        "git -C DIRECTORY remote add -t master -t dev -f upstream URL",
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			cs, restore := test.InitCmdStubber()
+			defer restore()
+
+			cs.Stub("") // git remote add -f
+
+			err := AddUpstreamRemote(tt.upstreamURL, tt.cloneDir, tt.branches)
+			if err != nil {
+				t.Fatalf("error running command `git remote add -f`: %v", err)
+			}
+
+			assert.Equal(t, 1, cs.Count)
+			assert.Equal(t, tt.want, strings.Join(cs.Calls[0].Args, " "))
+		})
+	}
 }
diff --git a/pkg/cmd/repo/clone/clone.go b/pkg/cmd/repo/clone/clone.go
index 73f4d7187..e6a10ead0 100644
--- a/pkg/cmd/repo/clone/clone.go
+++ b/pkg/cmd/repo/clone/clone.go
@@ -144,7 +144,7 @@ func cloneRun(opts *CloneOptions) error {
 		}
 		upstreamURL := ghrepo.FormatRemoteURL(canonicalRepo.Parent, protocol)
 
-		err = git.AddUpstreamRemote(upstreamURL, cloneDir)
+		err = git.AddUpstreamRemote(upstreamURL, cloneDir, []string{canonicalRepo.Parent.DefaultBranchRef.Name})
 		if err != nil {
 			return err
 		}
diff --git a/pkg/cmd/repo/clone/clone_test.go b/pkg/cmd/repo/clone/clone_test.go
index e7aa57b08..916c94304 100644
--- a/pkg/cmd/repo/clone/clone_test.go
+++ b/pkg/cmd/repo/clone/clone_test.go
@@ -218,6 +218,9 @@ func Test_RepoClone_hasParent(t *testing.T) {
 						"name": "ORIG",
 						"owner": {
 							"login": "hubot"
+						},
+						"defaultBranchRef": {
+							"name": "master"
 						}
 					}
 				} } }
@@ -237,7 +240,7 @@ func Test_RepoClone_hasParent(t *testing.T) {
 	}
 
 	assert.Equal(t, 2, cs.Count)
-	assert.Equal(t, "git -C REPO remote add -f upstream https://github.com/hubot/ORIG.git", strings.Join(cs.Calls[1].Args, " "))
+	assert.Equal(t, "git -C REPO remote add -t master -f upstream https://github.com/hubot/ORIG.git", strings.Join(cs.Calls[1].Args, " "))
 }
 
 func Test_RepoClone_withoutUsername(t *testing.T) {
diff --git a/pkg/cmd/repo/fork/fork.go b/pkg/cmd/repo/fork/fork.go
index 760bb6537..63cbf5129 100644
--- a/pkg/cmd/repo/fork/fork.go
+++ b/pkg/cmd/repo/fork/fork.go
@@ -273,7 +273,7 @@ func forkRun(opts *ForkOptions) error {
 			}
 
 			upstreamURL := ghrepo.FormatRemoteURL(repoToFork, protocol)
-			err = git.AddUpstreamRemote(upstreamURL, cloneDir)
+			err = git.AddUpstreamRemote(upstreamURL, cloneDir, []string{})
 			if err != nil {
 				return err
 			}