It comes after abuse on social media
A police investigation has been launched and the ban for both supporters will take effect immediately.
A statement from the Football Club says: "Exeter City has today banned two supporters indefinitely from games at St James Park following social media abuse directed at both a former player and manager of our club.
"Exeter City takes a zero-tolerance approach to all forms of abuse, both at the ground and online, especially those of a discriminatory or racist nature.
"The posts, made on Twitter and Facebook, fall well below the standard we expect from our supporters and have been reported to Kick It Out and the police."
Speaking last month in an interview with Radio Exe, about racism and abuse in football, Exeter City chairman Julian Tagg said: "Perpetrators should be punished in the most severe fashion. Behaviour like this needs to be stamped out the game."