Sidwell was forced off midway through the first half of Saturday's 1-0 Premier League defeat at Liverpool with the problem, with Stoke originally fearing he could be set for an even lengthier lay-off.
And in a press conference on Monday ahead of their trip to Manchester United 24 hours later, Hughes revealed that Sidwell would be out until at least the new year.
"Steve Sidwell has had a scan and he is likely to be out for four to six weeks," he said.
"It is a blow to us, especially with the games we have coming up. We initially feared it may be eight weeks or so, so in that aspect we are pleased because it isn't as serious as first feared."
Hughes also confirmed that Glenn Whelan - who replaced Sidwell at Anfield but was then substituted himself at half-time - would be out with a calf problem, although right-back Phil Bardsley will be fit to face his former club.
"Glenn is likely to be out for a couple of weeks too," he said.
"He will certainly miss the game tomorrow. Phil Bardsley trained today and we feel he should be ok for the game on Tuesday."
Hughes, who had two spells at Old Trafford during his playing days, is aware his side are in for a tough test on Tuesday as they come up against a team in buoyant mood following three successive league wins.
"Had we played them a few weeks ago then it may have been easier, because they looked a little vulnerable," he said.
"They have improved and they are playing really well at the moment. They are performing well and we have played well in general - even though results don't back that up.
"I really feel that it will be a good match. We will go there with the belief that we can take something from it."
