The 25-year-old was a major doubt for Friday's game anyway after suffering groin and toe injuries during Saturday's 2-1 Barclays Premier League win over Everton.
However, manager Alan Pardew also revealed after the game that his wife was due to give birth imminently, and it is understood he will remain on Tyneside before joining up with the rest of the squad on Saturday.
International boss Giovanni Trapattoni had earlier revealed his medical team were awaiting news of scans on the player's groin problem before making a decision on him.
Best's absence, coupled with those of the suspended Kevin Doyle and the injured Shane Long, has left Jonathan Walters and Simon Cox to battle it out for the task of partnering skipper Robbie Keane in Tallinn with Trapattoni hinting that the Stoke man could get the nod.
