The left-back was forced off during their 1-1 draw with Leicester City in the Premier League on 2 April. He was then sidelined from their Everton loss, too, on 9 April, but it now seems like the 26-year-old won't be returning to action anytime soon.
Shaw went under the knife last week to have metal bolts removed from his leg. The bolts were originally inserted during a surgery in 2015 after the Manchester United player broke his leg in a Champions League match against PSV Eindhoven.
Rangnick has now revealed that Shaw will be out for another four to five weeks in a huge blow for the Red Devils.
Speaking at the pre-match press conference ahead of United's Premier League clash against Norwich City on 16 April, Rangnick was quoted as saying by Metro:
"Shaw had his bolts and metal stuff removed from his leg. It seems like he will be out for another at least four weeks, if not five weeks. I think it will be difficult for him to be available for any of our remaining games."
Alex Telles, who's played 20 times this season, is likely to come in for him at the left-back position, with Phil Jones also an option.
In a further blow for Manchester United ahead of their clash with Norwich City, Fred, Scott McTominay, Raphael Varane and Edinson Cavani have also been ruled out.
Fred sustained a knock during their Everton defeat while McTominay has been nursing a foot injury since last week.
Varane, whose first season at the club since joining from Real Madrid has been riddled with injuries, developed muscular problems at the start of April.
Cavani also hasn't had much luck with fitness this season, with the Uruguayan missing 23 games in all competitions thus far.
Manchester United have been struck with a lot of fitness issues this season which has also affected their performances on the pitch.
Manchester United face uphill battle for top-four finish
Manchester United's terrible league campaign has continued under Rangnick. They now face an uphill battle to rescue a top-four spot in the Premier League with only seven games remaining this season.
The Red Devils are currently in seventh position with 51 points from 31 games, six off fourth-placed Tottenham, while Arsenal (54) and West Ham (51) are also in the running.
Rangnick's side will be desperate to pick up their first win of the month against Norwich, having drawn and lost in two games so far.
But if they're to finish inside the Champions League positions, United must put together a winning streak as there's no room for more errors.