The 25-year-old Newcastle United forward was already a major doubt for the game in Tallinn after suffering groin and toe injuries during Saturday's 2-1 Premier League win over Everton.
With Best, Liam Lawrence and Shane Long injured, and Kevin Doyle suspended, either Jonathan Walters or Simon Cox will partner skipper Robbie Keane in attack.
Coach Giovanni Trapattoni, hoping to guide Ireland into their first European finals since 1988, said Best would rejoin the squad on Saturday to prepare for the second leg in Dublin on November 15.
He also hopes John O'Shea could return to the squad for the second game.
"We will wait for him," said Trapattoni. "He is not fit for Friday's game, but will come with us on Saturday."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.