Vila had been due to join on loan for the 2012/13 season with Valencia having the option to make the deal permanent but the club discovered a pelvic injury during their medical tests on the left-back and have now called the deal off despite Milan waiving the loan fee.
The former Espanyol man had been signed to replace Jordi Alba who moved to Barcelona earlier in the summer but are now expected to make a move for either Malaga's Nacho Monreal or Jose Angel of Roma.
A statement on Valencia's website www.valenciacf.com read: "Didac Villa has not passed the medical tests that have been submitted by the medical staff of Valencia Football Club.
"The medics consider that he is not 100% fit to play football immediately. Therefore, Valencia FC has called off his transfer.
"The club wishes every success to this extraordinary player in his career."