Karen Gillan and Arthur Darvill have played the husband and wife team since Matt Smith took over the role of the time-traveling Doctor early last year.
"The final days of the Ponds are coming," Moffat said at a London screening of the "Doctor Who" Christmas episode.
"I'm not telling you when or how, but that story is going to come to a heartbreaking end."
The show-runner went on to say the Doctor was going to meet "a new friend" who has not yet been cast.
"We had the most incredible journey," Smith said of working with Gillan and Darvill. "We took over the show and we've really had to hold hands and help each other through it. So it's very disappointing, but one has to remember that this show is about change and regeneration, and that's what galvanizes it and pushes it forwards."
Smith is the 11th actor to play the Doctor on the long-running series.
Notable deaths of 2014 [PHOTOS]