Centre Graeme Morrison and No.8 Ryan Wilson have been assessed by an orthopaedic surgeon, with knee medial collateral ligament injuries diagnosed in both cases.
Morrison's is at the lower end of the scale, and the 29-year-old is expected to be unavailable for selection for approximately three weeks.
Wilson, meanwhile, is likely to be missing for around eight weeks.
Back row forward John Barclay, substituted in the Cardiff game after receiving a blow to the head, is recovering well and has resumed running under supervision. The 25-year-old will be subject to the usual IRB return to play protocols.
A club spokesman said: "The Glasgow Warriors medical team are working closely with Graeme, Ryan and John to ensure they receive the best possible support as they recover from their respective injuries."
The Warriors' bid to reach the RaboDirect PRO12 play-offs continues with a game against Munster in Cork on Saturday 14 April (kick-off 7.15pm, live on BBC ALBA).
We're giving supporters the chance to save money, time and hassle as they savour one of the biggest days in Glasgow rugby history, Saturday 5 May.
There's a feast of top class rugby and enjoyment on offer throughout the city, with the first day of the Emirates Airline Glasgow 7s taking place at Scotstoun Stadium, followed by the play-off chasing Warriors' huge RaboDirect PRO12 game against Connacht at Firhill.
Warriors fans can not only back their own team in their quest for the semi-finals, but get a taste of what will be the club's new playing base of next season.
We've put together a super saver joint ticket package covering these two great events, and are giving fans the option of including a bus transfer from Scotstoun to Firhill, where the Warriors match will kick-off at 7.30pm.
See www.glasgowwarriors.org or call 0844 800 3490 for more information and to book.
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland