Hughes, who has already lost Victor Moses for the season with a hamstring injury, is now set to be without Spanish central defender Muniesa for the foreseeable future.
Erik Pieters and Marc Wilson are also carrying knocks and may miss the visit of Southampton to the Britannia Stadium on Saturday.
Hughes told the club’s website: “Unfortunately we have lost Marc Muniesa today, to a slight problem with his hamstring.
“It is nothing like the injury he had four or five weeks ago, but because it has happened on a Friday he will miss out tomorrow.
“Marc Wilson unfortunately slipped over in training and landed on the wrist that he injured a couple of weeks ago, so that is disappointing.
“Obviously the pain has irritated him somewhat but hopefully that will settle down overnight and touch wood he will be OK to feature in the game.
But Hughes did have better news about Odemwingie, after the striker came through his first two days of full training following six months out with a knee injury.
“Peter has trained with the group fully in two sessions now, on Thursday and earlier today, and thankfully came through everything,” he added.
“We are delighted to have him back amongst the group again because we have missed him this season. He made a huge impact last season and we would have utilised him this year, I’m sure of that.
“We will bide our time with him, but we do want to get him on the pitch before the end of the season; that is the aim.”
“Erik (Pieters) has had an operation on his wrist too, and the ball hit in right on that hand towards the end of the session, so he is in a little bit of discomfort too.
“It’s not been the best season in terms of injuries, but I felt really hard done by today, losing three players – all of whom are candidates to start in the left-back position. Hopefully two of the three, Marc Wilson and Erik Pieters, will rest overnight and be available to me tomorrow.”