The midfielder was forced off just before half-time during Manchester United's 1-0 loss.
Cleverley's injury will be assessed on Thursday but Sir Alex Ferguson is not expecting a positive outcome.
"Tom felt his calf a little bit," said Ferguson. "We will assess it in the morning but it is not good news."
Ferguson has also ruled skipper Nemanja Vidic out of the visit to Manchester City, but central defensive colleague Jonny Evans could be available.
However, Japan midfielder Shinji Kagawa seems certain to miss out.
"Kagawa is a fantastic player," said Ferguson. "He is back doing some running but I don't know if he will make Sunday.
"At least he is training. Hopefully he will join in the football part on Monday."