The 31-year-old made the switch from Gloucester to Cardiff in 2009 but has since only made 22 appearances for the region.
This season he has only featured in two games, with the problem flaring up again.
"I've come to an amicable agreement with Cardiff Blues and would like to thank them for all their support over the years," said Cooper.
"It's been a frustrating couple of years for me and things haven't quite worked as I'd hoped. I don't think I've shown my full potential at the Blues due to the groin injury.
"I've been told by the medical team that I need a full rest from the game for between six to 12 months.
"The groin injury started to hurt in the summer of 2009 and it's got progressively worse. Throughout that period I'd been playing with a lot of pain and had to have two operations on the groin and then a double hernia operation.
"This season I've played 20 minutes against Treviso and started against Connacht but I had to take pain killers, so the doctors have recommended that I am to rest fully for up to a year.
"Obviously I will miss all the players and management who have been fantastic with me since I arrived and would like to wish them the best of luck for the future."
Former Lion and current Cardiff Blues chief executive Robert Norster was clearly disappointed by the news but has praised the scrum-half and wished him a successful future.
"It is hugely disappointing news for both Gareth and the Blues that such a talented player is sidelined in this way," said Norster a two-time Lions tourist in the 1980's.