diff --git a/cli/command/container/completion.go b/cli/command/container/completion.go
index 97d32728fa84..5b1816d2997f 100644
--- a/cli/command/container/completion.go
+++ b/cli/command/container/completion.go
@@ -18,6 +18,24 @@ import (
 // allCaps is the magic value for "all capabilities".
 const allCaps = "ALL"
 
+// completeCopy delegates local path completion to the shell. Container paths
+// cannot be completed from the local filesystem.
+func completeCopy(_ *cobra.Command, args []string, toComplete string) ([]string, cobra.ShellCompDirective) {
+	if len(args) >= 2 || toComplete == "-" {
+		return nil, cobra.ShellCompDirectiveNoFileComp
+	}
+	if ctr, _ := splitCpArg(toComplete); ctr != "" {
+		return nil, cobra.ShellCompDirectiveNoFileComp
+	}
+	if len(args) == 1 {
+		if ctr, _ := splitCpArg(args[0]); ctr == "" {
+			// A local source (including stdin) requires a container destination.
+			return nil, cobra.ShellCompDirectiveNoFileComp
+		}
+	}
+	return nil, cobra.ShellCompDirectiveDefault
+}
+
 // allLinuxCapabilities is a list of all known Linux capabilities.
 //
 // TODO(thaJeztah): add descriptions, and enable descriptions for our completion scripts (cobra.CompletionOptions.DisableDescriptions is currently set to "true")
diff --git a/cli/command/container/cp.go b/cli/command/container/cp.go
index 52fc06ab3e21..aa59d19a24ac 100644
--- a/cli/command/container/cp.go
+++ b/cli/command/container/cp.go
@@ -154,6 +154,7 @@ container source to stdout.`,
 		Annotations: map[string]string{
 			"aliases": "docker container cp, docker cp",
 		},
+		ValidArgsFunction:     completeCopy,
 		DisableFlagsInUseLine: true,
 	}
 
diff --git a/cli/command/container/cp_test.go b/cli/command/container/cp_test.go
index d2ce73b0d30d..2d28d9b85470 100644
--- a/cli/command/container/cp_test.go
+++ b/cli/command/container/cp_test.go
@@ -1,10 +1,13 @@
 package container
 
 import (
+	"bytes"
 	"context"
 	"errors"
+	"fmt"
 	"io"
 	"os"
+	"path/filepath"
 	"runtime"
 	"strings"
 	"testing"
@@ -14,11 +17,65 @@ import (
 	"github.com/moby/go-archive/compression"
 	"github.com/moby/moby/api/types/container"
 	"github.com/moby/moby/client"
+	"github.com/spf13/cobra"
 	"gotest.tools/v3/assert"
 	is "gotest.tools/v3/assert/cmp"
 	"gotest.tools/v3/fs"
 )
 
+func TestCopyCompletion(t *testing.T) {
+	absolutePath := filepath.Join(t.TempDir(), "file")
+	if runtime.GOOS != "windows" {
+		absolutePath += ":name"
+	}
+	tests := []struct {
+		name      string
+		args      []string
+		directive cobra.ShellCompDirective
+	}{
+		{name: "empty source", args: []string{""}},
+		{name: "relative source", args: []string{"./"}},
+		{name: "source in home directory", args: []string{"~/"}},
+		{name: "absolute source with colon", args: []string{absolutePath}},
+		{name: "relative source with colon", args: []string{"./file:name"}},
+		{name: "container source", args: []string{"example:/tmp/"}, directive: cobra.ShellCompDirectiveNoFileComp},
+		{name: "empty container path", args: []string{"example:"}, directive: cobra.ShellCompDirectiveNoFileComp},
+		{name: "stdin source", args: []string{"--", "-"}, directive: cobra.ShellCompDirectiveNoFileComp},
+		{name: "empty local destination", args: []string{"example:/tmp/file", ""}},
+		{name: "relative destination", args: []string{"example:/tmp/file", "./"}},
+		{name: "destination in home directory", args: []string{"example:/tmp/file", "~/"}},
+		{name: "absolute destination with colon", args: []string{"example:/tmp/file", absolutePath}},
+		{name: "container destination", args: []string{"./file", "example:/tmp/"}, directive: cobra.ShellCompDirectiveNoFileComp},
+		{name: "destination after local source", args: []string{"./file", ""}, directive: cobra.ShellCompDirectiveNoFileComp},
+		{name: "destination after stdin", args: []string{"-", ""}, directive: cobra.ShellCompDirectiveNoFileComp},
+		{name: "stdout destination", args: []string{"--", "example:/tmp/file", "-"}, directive: cobra.ShellCompDirectiveNoFileComp},
+		{name: "extra argument", args: []string{"example:/tmp/file", "./file", ""}, directive: cobra.ShellCompDirectiveNoFileComp},
+	}
+	for _, commandPath := range [][]string{{"cp"}, {"container", "cp"}} {
+		t.Run(strings.Join(commandPath, " "), func(t *testing.T) {
+			for _, tc := range tests {
+				t.Run(tc.name, func(t *testing.T) {
+					root := &cobra.Command{Use: "docker"}
+					root.CompletionOptions.SetDefaultShellCompDirective(cobra.ShellCompDirectiveNoFileComp)
+					parent := root
+					if len(commandPath) == 2 {
+						parent = &cobra.Command{Use: "container"}
+						root.AddCommand(parent)
+					}
+					parent.AddCommand(newCopyCommand(test.NewFakeCli(nil)))
+					var out bytes.Buffer
+					root.SetOut(&out)
+					root.SetErr(io.Discard)
+					args := append([]string{cobra.ShellCompNoDescRequestCmd}, commandPath...)
+					root.SetArgs(append(args, tc.args...))
+					assert.NilError(t, root.Execute())
+					assert.Equal(t, out.String(), fmt.Sprintf(":%d\n", tc.directive))
+				})
+			}
+		})
+	}
+}
+
 func TestRunCopyWithInvalidArguments(t *testing.T) {
 	testcases := []struct {
 		doc         string
diff --git a/docs/reference/commandline/container_cp.md b/docs/reference/commandline/container_cp.md
index 8d8958bb37b7..c71cf8e3e4b8 100644
--- a/docs/reference/commandline/container_cp.md
+++ b/docs/reference/commandline/container_cp.md
@@ -40,6 +40,9 @@ be an absolute or relative value. The command interprets a local machine's
 relative paths as relative to the current working directory where `docker cp` is
 run.
 
+When shell completion is enabled, `docker cp` completes local file and directory
+paths. Completion of paths inside containers is not supported.
+
 The `cp` command behaves like the Unix `cp -a` command in that directories are
 copied recursively with permissions preserved if possible. Ownership is set to
 the user and primary group at the destination. For example, files copied to a