Up front, Frankie Sheahan comes in for the injured Flannery at hooker, while Niall Ronan gets the nod ahead of John O'Sullivan.
Murphy's inclusion sees him team up with Lifeimi Mafi in the centre with Keith Earls moving to full-back.
With Ronan wearing the number 7 jersey, Donnacha Ryan, along with James Coughlan, provides strong back row cover from the bench.
Despite the surprise defeat of Sunday's opposition by Mont-de-Marsan, Munster lock Donncha O'Callaghan anticipates a huge challenge in Clermont.
"If anything, that defeat will probably make them even more determined. Besides that, they'll be looking to put one over on us for last season when we effectively stopped them making the knock-out stages," he said.
"I've never played a game in France that wasn't hugely demanding and this one will be right up there with internationals in terms of speed, intensity, physicality anything you care to mention."
Munster come into the game on foot of a narrow Magners League win over the Scarlets albeit with a less than convincing second half performance - a fact not lost on captain Paul O'Connell.
"While it was a huge boost to get a win last week, we know our second half performance wasn't what was required," he said.
"I thought though that we showed huge character to get back down there after the penalty try and then Rog (Ronan O'Gara) did the rest as only he can.
"Of course we'd be realistic, disappointed with that second half but to keep producing performances you have to be emotional and passionate week in, week out and that's a hard thing to do. A very hard thing to do.
"That's why the Magners League is so important. It gives lads the opportunity to put their hands up and I think we've seen that happen the past few weeks.
"No side in this competition or anywhere could be happy losing the likes of Rua, Denis Hurley, Jerry or Leamy on an individual basis, never mind at the same time.
"But we have 30 odd players hungry to be in the starting fifteen and that can only be a good thing. I think that's an indicator that our squad is stronger now than it has been in the past," O'Connell added.
Sunday's game kicks off at 3pm Irish time/4pm local time and will be broadcast live on Sky Sports 2.
MUNSTER (v Clermont Auvergne): Keith Earls; Doug Howlett, Barry Murphy, Lifeimi Mafi, Ian Dowling; Ronan O'Gara, Tomas O'Leary; Marcus Horan, Frankie Sheahan, John Hayes, Donncha O'Callaghan, Paul O'Connell (capt), Alan Quinlan, Niall Ronan, David Wallace.
Replacements: Denis Fogarty, Tony Buckley, Donnacha Ryan, James Coughlan, Peter Stringer, Paul Warwick, Kieran Lewis.