You usually say something similar, with a 네 (okay) as an acknowledgement.
- 네, 안녕히 주무세요.
- 네, 잘 자요. (more informal)
- 네, 좋은 꿈 꿔요 ("Have a good dream" - if you want to say something different)
- 네, 내일 봐요 ("See you tomorrow" - if you're going to see them tomorrow).