But Newcastle rugby director John Fletcher moved to allay fears Tait could be ruled out of contention for the November 5 All Blacks tussle.
"Mathew was due to start the game on Saturday because he is short of match action, but unfortunately, during the win over Padova last Friday he got a small tear in one of his quad muscles," said Fletcher.
"We could have risked him and he may well have got through the Brive game, but that is not in anyone's interests long-term.
"He will be fine for next week with England, should he be selected."
Fletcher has decided to rest Tait's Newcastle - and possible England - midfield partner Jamie Noon when Falcons go in search of a second successive Pool Three win on a ground where they triumphed 24-17 last season.
"It was always part of the planning to rest Jamie this weekend," added Fletcher.
"He has been awesome for us so far this season, and resting him is the right thing to do for everyone concerned to keep him at his best."
Toby Flood, one of seven uncapped players in Andy Robinson's 30-man squad for the New Zealand game, starts at fly-half.
Bath and Harlequins could effectively make Pool Four a two-team race between themselves if they beat respective visitors Connacht and Montpellier tomorrow, but Saracens will need an improvement on last weekend's stuttering Pool Two victory over Glasgow to trouble French hosts Narbonne.
Worcester have undoubtedly the toughest test of England's representatives, visiting Pool Five favourites Clermont Auvergne, who lie second in the French Championship.
"They are a well-balanced side across the park," said Worcester coach Anthony Eddy. "They are exceptionally strong at forward, and possess some classy and speedy players behind the scrum."
Bristol head coach Richard Hill has named a powerful starting XV, including England scrum-half hopeful Shaun Perry, former Lions hooker Mark Regan and Wales second-row veteran Gareth Llewellyn, for Friday night's Pool One encounter against Memorial Stadium visitors Newport Gwent Dragons.
Hill has demanded a vastly-improved effort after the Guinness Premiership leaders struggled to put away Bucuresti last Saturday.
"We tried to play fancy rugby against Bucuresti without doing the hard graft first," said Hill.
"I was disappointed because we had talked about it beforehand. I can't explain the errors - I think maybe we had believed our own publicity a bit.
"I hope we have learned the lesson - we've had a kick up the backside. We will not be able to squander quality scoring chances against Newport Gwent Dragons. They are far too good for that."
The Dragons side features Wales autumn Test squad members Kevin Morgan, Ceri Sweeney, Gareth Cooper and Ian Gough, while back-row pair Colin Charvis and Michael Owen will look to make statements after being left out of the 32-man group.