The Warriors must beat last season's Heineken Cup finalists Perpignan at the Brewery Field on Friday night to keep alive hopes of reaching the last eight.
But Wales outside-half Sweeney fears former Wallaby Edmonds - who single-handedly knocked out the Scarlets last year - could do the same again.
"He's the sort of player who can make something out of nothing, he's a class act," said Sweeney.
"I have watched over the years ever since he played against the Lions in 2001 and he is still as good now as then.
"He's a very skillfull kicker, a good runner and someone we will really have to keep an eye on."
Sweeney starts ahead of Neil Jenkins for the Warriors who have made four changes, one positional, to the side edged out by Wasps last weekend.
Wales partner Gareth Cooper takes over at scrum-half while Robert Sidoli and prop Chris Horsman both return from injury to play their first games of the year. That allows Gethin Jenkins to return to his favoured loosehead side of the front-row.
Coach Lynn Howells said: "We lacked some bulk and lineout presence against Wasps but we have got that back as well as having a replacements bench that can make a difference."
Howells, meanwhile, has put his weight behind Gareth Jenkins' application for the Wales job.
The Warriors team boss added: "Gareth is the man the coaches want and the players want and I think he would do an excellent job."
Celtic Warriors: G Wyatt; D James, S Parker, G Thomas (capt), A Havili; C Sweeney, G Cooper; G Jenkins, M Davies, C Horsman, D Jones, R Sidoli, M Molitika, C Harris, R Parks
Replacements: M Rees, C Loader, B Cockbain, N Kelly, S Martens, N Jenkins, J Bryant
Perpignan: F Cermeno; P Bomati, D Marty, C Manas, D Luger; M Edmonds, J Fillol; P Freshwater, N Grelon, N Mas, C Gaston, V Debaty, L Mallier, B Goutta (capt), M O'Driscoll
Replacements: A Moreno, F Tournaire, G Le Corvec, J Labat, L Loustau, P Giordani, T Stimpson
Referee: Giulio de Santis (Italy)