Best will return home as soon as he is released from the Bordeaux hospital where he spent Wednesday night after suffering a loss of sensation down his right side, a mild headache and a difficulty in speaking.
The results of tests on Best and a diagnosis of what he suffered from were not yet available.
"The thoughts of the management and all the players are with Simon at this time," coach Eddie O'Sullivan said.
"He is an incredibly popular player and is a key member of the squad and it was a shock to everybody when we heard the news."
Munster prop Tony Buckley has been called up as a replacement for Best while Bryan Young moves up into the match squad for Sunday's Pool D game against Argentina.
O'Sullivan has yet to name his hooker for the match with the IRU saying a decision would be taken once Jerry Flannery and Rory Best have completed fitness tests later on Thursday.
Best, 29, made three appearances off the bench in the tournament against Namibia, Georgia and France.