Bale's fitness has been a source of concern for the national side since he suffered a calf muscle strain against Borussia Dortmund in the Champions League last week.
"The Football Association of Wales can confirm that Gareth Bale will miss the upcoming World Cup qualifiers against Georgia and Republic of Ireland," said an FAW statement
"Bale -- who missed Real Madrid's game against Espanyol on Sunday -- arrived with the rest of the Wales squad on Sunday and attended yesterday's annual FAW Awards dinner at the team headquarters in Cardiff.
Wales are currently second in Group D, four points behind leaders Serbia and one point above Ireland.
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Two wins in the matches on Friday, away to Georgia, and next Monday, at home to Ireland, are likely to guarantee them at least a place in next month's play-offs for a place in Russia.
Bale's absence could open the door for Liverpool teenager Ben Woodburn to make his first Wales start.
The 17-year-old made a dramatic introduction last month when he scored the winner within five minutes of coming on as a second-half substitute against Austria.