Connacht Academy graduate Tiernan O'Halloran will take Matthews' place on the province's replacements bench for this evening's Magners League match at the Sportsground.
Connacht head coach Eric Elwood said: "We're all very disappointed for Keith. He's put in a tremendous amount of work and has been an integral part of our achievements this year.
"He was really looking forward to finishing the season on a high but unfortunately it looks like he'll be out for a good chunk of the year now.
"It's a good opportunity for one of our homegrown talents, Tiernan, to step up now and we'd like to wish Keith a speedy recovery."
CONNACHT (v Cardiff Blues): Gavin Duffy; Brian Tuohy, Niva Ta'auso, Troy Nathan, Fionn Carr; Ian Keatley, Frank Murphy; Ronan Loughney, Sean Cronin, Jamie Hagan, Mike McCarthy, Bernie Upton, Andrew Browne, Johnny O'Connor (capt), Ray Ofisa.
Replacements: Adrian Flavin, Brett Wilkinson, Rodney Ah You, Mike McComish, John Muldoon, Mark Dolan, Tiernan O'Halloran, Eoin Griffin.