The striker picked up a groin problem prior to the 4-1 defeat to Manchester City on Sunday, and will now miss the game at Old Trafford.
However, David Moyes believes Van Persie has an "outside chance" of featuring against West Brom in the Premier League on Saturday.
| MANCHESTER UNITED LATEST
|6/1||Man Utd are 6/1 with Paddy Power to win both halves v Liverpool
Moyes also believes it is time to move on from their convincing derby defeat and expects to learn more about his players' character in the coming weeks.
He continued: "It's gone now. I can't do anything about it so we move on and get ready for the next game.
"I'm still getting to know all the players. I'll get to know a few more this week and see what they can do."
Despite Van Persie absence, Moyes hinted that he will include a number of established players for the Capital One Cup clash, a match which could mark Luis Suarez's return to competitive action for Merseyside outfit.
"It's a big rivalry," he added. "And it could take on a bigger significance than people might expect.
"I think it means that Liverpool have a got a really good player. Does it change the complexion? I don't know. I'm not looking at Liverpool too much except that I know the quality of Luis Suarez is very good."
"The cup has been a route to giving young players an opportunity. [But] obviously this is a really big tie."