The 28-year-old was left out of Real Madrid's 2-0 La Liga win over Espanyol last Sunday with a calf problem, although head coach Zinedine Zidane insisted there was no major concern about his fitness.
However, further tests with the Wales medical staff have determined he will not be available for his side's final two matches in Group D.
The Football Association of Wales confirmed it sent Bale for scans after a consultation with Madrid, which showed his injury is taking longer to heal than was hoped.
Barnsley striker Tom Bradshaw has been called up in his place and will join up with the squad on Tuesday.
Wales sit second in the group, four points behind leaders Serbia and one ahead of the Republic of Ireland in third.
A win over Georgia and a draw in Cardiff will guarantee a place in the play-offs for next year's finals in Russia.