The 25-year-old has failed to secure a regular place in the City side since his move to the Etihad Stadium from Swansea City in 2012 and has made only two appearances in the league this season.
Sinclair spent last season on loan at West Bromwich Albion, making 11 appearances in all competitions.
Champions City said the temporary deal with Villa could be made permanent at the end of the campaign.
"I am still hungry to play football, that's what I told him (Villa manager Paul Lambert), and I'm looking forwarding to getting started, hopefully playing every week and enjoying my football," Sinclair said in a statement on Villa's website (www.avfc.co.uk).
"I believe I have my best years ahead of me. This is a new challenge, a new chapter in my life, and hopefully I can settle in as quickly as possible, have a good start and go from there."
(Reporting by Sam Holden, editing by Ed Osmond)
