Welsh international Rees is recalled in the front row and is one of eight changes made by Director of Rugby Mark Hammett to the side that narrowly lost out to champions Leinster last week.
Tight-head prop Taufa’ao Filise makes his first start of the campaign, with Adam Jones rested, while Gethin Jenkins packs down at loosehead.
Samoa international Filo Paulo returns to partner All Blacks ace Jarrad Hoeata in the second row while the back row sees Macauley Cook and Manoa Vosawai called in to play alongside Sam Warburton. Josh Turnbull moves to the replacements bench.
Three changes in the backs include Adam Thomas being named at full back, with the league’s current highest scorer Rhys Patchell moving to fly half.
Dan Fish returns on the wing while fit-again Gavin Evans joins forces with Cory Allen in midfield.
“We know Connacht is a tough place to go and play,” said Hammer. “It’s a hard assignment out in Galway, with the travel and potential weather conditions. But both teams are playing in it and we have got to deal with it.
“We have made improvements to our game every week this season and this is another fixture when we try and build on that.
“We were disappointed last weekend as we should have definitely taken a bonus point against Leinster,” he added. “We had a situation where we had revived ourselves, were four points down and had momentum going our way. It was disappointing not to get a point or even a win.
“Now we need to continue to improve all aspects of our game. At the moment we are a team that has gone well in certain areas but haven’t put it together over 80 minutes. That needs to change.
“A win would certainly build confidence, there is no doubt about that, but we are looking at the big picture here and taking another step forward as a team at Connacht.”
Cardiff Blues: 15 Adam Thomas, 14 Alex Cuthbert, 13 Cory Allen, 12 Gavin Evans, 11 Dan Fish, 10 Rhys Patchell, 9 Lewis Jones; 1 Gethin Jenkins, 2 Matthew Rees (c), 3 Taufa’ao Filise, 4 Jarrad Hoeata, 5 Filo Paulo, 6 Macauley Cook, 7 Sam Warburton, 8 Manoa Vosawai
Replacements: 16 Kristian Dacey, 17 Sam Hobbs, 18 Scott Andrews, 19 Josh Turnbull, 20 Josh Navidi, 21Tavis Knoyle, 22 Gareth Davies, 23 Geraint Walsh