Midfielder Anderson has sustained an ankle injury and will be sidelined for about three weeks.
Defender Jonny Evans also picked up an ankle injury and he will also be sidelined for the same period.
Striker Nani suffered a groin strain which is expected to have healed in about a week.
"We sent Anderson for a scan and there's no break," Fergie said on Friday morning.
"There was some ligament damage so we think he'll be out for three weeks.
"Nani suffered a groin injury and he'll be out for a week.
Jonny Evans will be out for three weeks."
That leaves the United boss without nine memebers of his first team squad for the FA Cup 4th Round tie against Tottenham this weekend.
"The ones who are out are Rio Ferdinand, Anderson, Nani, Rafael, Patrice Evra, Wayne Rooney, Wes Brown, Jonny Evans and Ji-sung Park," Fergie added.
"We will have to call on some young players.
"It's not the best position to be in because January is a difficult month."