Owen was expected to start Tuesday's Carling Cup tie against Wolves after recovering from a recent groin complaint.
However, the 30-year-old was a late absentee from the team and has confirmed he has now picked up a fresh muscle problem.
"I've trained for a week and had a setback with another muscle injury," said Owen.
"I've got some damage in my hamstring and will be out for the next few weeks unfortunately."
The former Liverpool forward has not featured for United since he was replaced at half-time during the 0-0 draw at Sunderland at the start of the month.
His outing at the Stadium of Light was his first start in the Premier League this season, although he did come off the bench to score the equaliser against Bolton in September.
Owen's only other competitive start for United this term was in the third round of the Carling Cup when he scored twice in a 5-2 success away to Scunthorpe.
He missed the closing months of last season with a hamstring injury suffered in the Carling Cup final and will hope he can soon return to Sir Alex Ferguson's disposal.