A scan this week will confirm the full extent of the damage but already Connacht coach Michael Bradley has resigned himself to the fact that he will be without Matthews for the remainder of this season.
The former Irish U-21 can play in the centre or on the wing but will now face a long period on the sideline.
"It is very unfortunate but I think everyone in the ground feared the worst when he got injured," said Connacht coach Michael Bradley.
Matthews played in 13 of Connacht's 16 games this season but is not likely to play again until the start of next season.
"Keith is a quality professional. He faces a tough time in the next few months but I know he will deal with it and will come back in flying form," added Bradley.
Meanwhile Flanker John Muldoon cracked his cheekbone during Sunday's encounter with Munster, while lock forward David Gannon damaged ankle ligaments in the early stages of the same game.
Muldoon (24) and Gannon (23), both of whom have played in all 16 Connacht games this year, will miss the remaining European Challenge Cup games at home to Bath on Friday week and away to Harlequins a week later.
The two will also miss the trip to Murrayfield to play Edinburgh at the end of January but are hopeful they will be back for Connacht's next game against the Ospreys in the Liberty Stadium on February 16.
If not, they should be available for the visit of Borders on March 2nd.
