Play was suspended just nine minutes into the contest when smoke was spotted coming from the back of the Stagecoach Stand, forcing fans onto the pitch while emergency services investigated the issue.
A club statement confirmed: "At 3.09pm today play was halted at St James Park during Exeter City vs. Carlisle United due to a smoke grenade being deployed behind the old Stagecoach Stand.
"Security were quick to respond to the emergency, moving spectators onto the pitch. Fire stewards and subsequently the fire brigade checked all areas and confirmed that the grandstand was safe. Police also moved swiftly in arresting the offender, who is now in custody.
"Play resumed approximately an hour later. The club expresses its thanks for the professionalism of the stewards, fire brigade and police."
The game restarted at 4.18pm with the hosts 1-0 up thanks to an early goal from Jayden Stockley.