The Premier League club said on their website that a scan had shown no significant bone or ligament damage to the player's leg.
"We are very pleased that the extent of his injury is less severe than first feared and is limited to bruising to the bone and soft tissue damage," Newcastle said.
"Depending on the speed of his recovery he should be fit to play again in early April."
The France Under-21 international will be assessed further in the coming days.
"He has been very lucky that he has not suffered more serious injury and this positive diagnosis in no way lessens the club's views with regard to the severity of the tackle from which it resulted," the club added.
Haidara, who told a French newspaper afterwards that he thought the tackle had ended his career, had to be carried off on a stretcher on Sunday following the first-half challenge.
Referee Mark Halsey missed the incident and the FA said it would not take retrospective action against McManaman, a decision Newcastle managing director Derek Llambias said showed English football's disciplinary procedures were not fit for purpose.
Wigan owner Dave Whelan caused further criticism this week when he defended McManaman and described the tackle as a 'fair challenge'.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.