Kinkaid signed a one-year, $1.75-million contract with the Habs over the summer to back up Carey Price, but he hasn't had much success in the early stages of the 2019-20 season.
The 30-year-old owns a 1-1-3 record along with a .875 save percentage, allowing at least four goals in five of his six appearances so far.
"Listen, I think it gives him the opportunity, if he passes through waivers, to have a chance to play more often in (AHL) Laval and hopefully to get his game back in sync," head coach Claude Julien said, according to Sportsnet's Eric Engels. "What we've seen from him is good, but maybe not good enough for this instant.
"We need a goaltender who - especially when we call on them infrequently - is making sure he's on top of his game."
Montreal lost its eighth consecutive contest Sunday in Boston and returns to action Tuesday against the New York Islanders.