The club say the pair admitted their involvement in directing abuse at Shamrock Rovers manager Stephen Bradley at a game last week and have apologised for their behaviour.
Investigations are ongoing and City say they have offered their full support and cooperation.
The club say they have no a zero tolerance policy to verbal abuse and have commended everyone who has supported Stephen Bradley and his family following the incident.
Club Statement. #CCFC84 pic.twitter.com/SLwKft9Vhj
— Cork City FC (@CorkCityFC) June 1, 2023