diff --git a/.changelog/24244.txt b/.changelog/24244.txt
new file mode 100644
index 000000000..c4668f6e6
--- /dev/null
+++ b/.changelog/24244.txt
@@ -0,0 +1,3 @@
+```release-note:bug
+docker: Fixed a bug where alloc exec could leak a goroutine
+```
diff --git a/drivers/docker/driver.go b/drivers/docker/driver.go
index c2e64567d..e410cc3df 100644
--- a/drivers/docker/driver.go
+++ b/drivers/docker/driver.go
@@ -1836,7 +1836,11 @@ func (d *Driver) ExecTaskStreaming(ctx context.Context, taskID string, opts *dri
 	if err != nil {
 		return nil, fmt.Errorf("failed to attach to exec: %v", err)
 	}
-	defer resp.Close()
+	defer func() {
+		opts.Stdin.Close() // close stdin
+		resp.CloseWrite()  // close hijacked write connection
+		resp.Close()       // close read connection
+	}()
 
 	go func() {
 		if !opts.Tty {