The Portugal international left the field in Sunday's 2-2 draw with Chelsea in their FA Cup quarter-final.
"We thought it could have been another bad hamstring injury but it is a slight one. He won't be ready for Sunderland [on March 30] but certainly the game after that," Ferguson told a news conference.
Giving his first news conference since the FA Cup game, he took the chance to dismiss Chelsea manager Rafael Benitez's accusation that he had refused to shake the Spaniard's hand before the game.
"It is nonsense. Why would I refuse to shake his hand?" the Scot said.
"I was signing autographs and I never saw him. Why he has said that I have no idea. If he wanted to shake hands he could have stood straight in front of me."
McDermott's dismiss has been hugely unpopular with Reading fans and Ferguson also questioned the timing.
"To sack Brian McDermott at this time of year was I thought strange to say the least," he said.
"If they had done it in December or the beginning of January maybe you would have understood it because it would have given the new manager time to get players in in the [transfer] window.
"[He was Premier League] manager of the month in January - all I can say is I hope I am not manager of the month this month!"
