Onomah, who Bruce had at Aston Villa last season, has only played once since the 58-year-old's late-January arrival at Hillsborough due to a hamstring problem.
The England Under-21 international returned to Tottenham for treatment but was pictured back training with his Sheffield Wednesday teammates on Thursday.
However, when asked if Onomah could feature in Wednesday's visit of Blackburn this weekend, Bruce replied via the Owls' official Facebook page: "He won't be available for Saturday. We're hoping that he will be available for Stoke in a couple of weeks.
"And it'll be good to see Josh back. He played very, very well for me at Aston Villa. And it's fair to say with the number of appearances he's made here, it hasn't gone as well as either party would like.
"But I'm a big admirer of Josh and I'm pleased that he's up and running and hopefully he'll have some part to play in the next eight games."
Onomah has only played 12 times for Sheffield Wednesday but has set up three goals nonetheless.
The Tottenham talent is one of several players the Owls have missed in recent weeks, despite the club's surge towards an unexpected top-six finish.
However, Bruce revealed that some of those, including strikers Lucas Joao and Gary Hooper, could make their return after the international break.
Joost van Aken will not play again this season, though, according to his manager.
How big a boost is the Tottenham man's return for Sheffield Wednesday?