The former Friends star's eight-year-old daughter Coco handed her the present on 25 December (12), as her ex-husband David Arquette looked on, and she still has no idea who it was from.
It led to an awkward few moments.
She explains, "It was a big pillow and it said 'Tonight' and on the other side it said 'Not tonight' and I was like, 'Well, who is going to be tonight and why not tonight. It was so confusing.
"David was also there with me and I was like, 'This is so odd. I don't know who to do it with tonight...' I just didn't know who the person was I was saying 'not tonight' to. It was a weird gift from someone I didn't know... It was awkward."
Cox chatted about the gift during an appearance on U.S. talk show Conan on Monday night (07Jan13) in the hope that the giver would come forward.
She said, "Maybe this will help."