The 32-year-old arrived at the Midlands outfit from West Ham United in June, but has only featured once for Villa in their 1-0 defeat to Leyton Orient in the Capital One Cup last month.
"It's been frustrating being injured but that is part and parcel of being a footballer," Cole told the club's official website. "There aren't many footballers that don't get injured.
"There's never a good time to be out but mine has come at the start of the season with my new club. It's been frustrating as motivation is high with me and I want to do well for my new club and my new team. I want to make an impact here at Villa."
In the Premier League, Villa are currently third in the table after five games.