The Irish management are hopeful that the 29-year-old will be fit to return to action shortly but have decided to bring Munster's Mike Sherry to New Zealand just in case.
Sherry, who is third choice at his province behind Jerry Flannery and Damian Varley, will join up with the squad this week but won't officially be added to the 30-man party unless Best is ruled out of a potential semi-final against England or France.
"Rory Best is still progressing with his rehabilitation this week," said Ireland manager Paul McNaughton.
"While he is still rated doubtful for the Wales game, we felt it was prudent to bring Mike Sherry down to New Zealand as precautionary cover.
"We expect Mike to arrive in New Zealand on Thursday."
Best started three of Ireland's pool games, including the 15-6 triumph over the Wallabies, and his potential absence is a big blow for Declan Kidney and co.
Ireland lost Flannery to injury before the tournament had already begun, meaning third-choice hooker Sean Cronin is likely to start against Wales, with Varley on the bench.
While Best hasn't officially been ruled out of the quarter-final, Irelandkicking coach Mark Tainton has confirmed that it is highly unlikely he will play any part in Wellington at the weekend.
"His chances at the moment, they're long. He's doubtful for this weekend but he's not ruled out of the competition," said Tainton.