The club was without O'Dea for Saturday's 3-0 loss to Sporting Kansas City as the team finalized the defender's transfer to a team in Ukraine.
After the game, manager Ryan Nelsen explained that shedding O'Dea's hefty contract — in the $450,000 range — would free up TFC's options.
"Darren has moved on. He got a contract from Ukraine that he couldn't turn down," Nelsen said in a interview on the team's website. "Darren's the most expensive player in the whole of the league, in terms of salary cap. It frees up some space for us. He wanted to go, it was a good opportunity for him.
"Unfortunately for Darren it's not his fault. His contract was pretty ridiculous, in terms of MLS contracts."
The 26-year-old Ireland international had a lucrative offer from Ukraine prior to joining Toronto last season.
The move comes days after Toronto traded midfielder Luis Silva to D.C. United for allocation money that can go toward cap relief. On Friday, defender Danny Califf announced his retirement.
The transfer also opens up an international spot, which is the second one acquired this month following a trade with Chivas USA.
O'Dea has one goal and one assist through 17 games with TFC this season. He last played for Toronto on July 3, a 3-3 draw with the Montreal Impact at BMO Field, where he scored his only goal of 2013.
O'Dea began his career with Celtic in the Scottish Premier League in 2006 and has represented Ireland at the under-21 and senior level.
Fellow defender Steven Caldwell wore the captain's armband for TFC in Saturday's loss in Kansas City.