The club announced it will work with the PFA, EFL and the police to seek, ban and prosecute any person found to have sent racist messages.
Owner and executive chairman Doug King said: “The messages sent to Fankaty were disgusting and there is no place for any person who sent such vile abuse at any of our games, and social media is not a hiding place to make these comments.
“The club and our partners will support Fankaty, and we will not hesitate in taking action against those people found to have done this.”
Coventry also confirmed the defender will leave the club at the conclusion of his contract alongside Julien Dacosta, Todd Kane, Sean Maguire, Michael Rose, Martyn Waghorn and Tyler Walker.
Loan players Jonathan Panzo, Callum Doyle, Brooke Norton-Cuffy, Josh Wilson-Esbrand and Luke McNally will return to their parent clubs.
Manager Mark Robins thanked those leaving and paid tribute to Dabo and Rose for playing key roles in Coventry’s League One success in 2019-2020.
He told the club website: “I would like to thank those who are leaving for their time with us, the contributions that they have made to Coventry City, and wish them all of the best for their future careers.
“In particular, Fankaty Dabo and Michael Rose were huge parts of the side that won the League One title and then established us in the Championship.
“They will both be fondly remembered for many years to come by all Sky Blues fans, and the outpouring of support for Fanky (Dabo) from our supporters following Saturday goes to show the esteem he is held in.”