Manager Steve Bruce feared the 18-year-old had damaged ligaments when he went down in agony at Old Trafford just seconds into last weekend's 1-0 Barclays Premier League defeat.
However, initial scans suggested the damage was not as serious as first thought, and further examinations have revealed no lasting problem.
A statement released via the club's official website read: "Sunderland have announced that further investigations have shown that Connor Wickham has not suffered any serious damage to his knee.
"The player has embarked on a rehabilitation programme as he recovers from the injury.
"Wickham left the field at Old Trafford after just 90 seconds on Saturday and underwent scans on Monday."
The news means that the former Ipswich frontman is expected to be missing for weeks rather than months, and that represents a major boost for Bruce.
Had the teenager been sidelined for an extended period, that would have left his manager with just two fit strikers at his disposal, loan signing Nicklas Bendtner and summer arrival Ji Dong-won, with Asamoah Gyan out on loan in the United Arab Emirates and Fraizer Campbell still some distance away from his own return from a knee problem.