Issara Somchai, a key leader of the anti-government People's Democratic Reform Committee (PDRC), said he heard an explosion at 3.47am at the Chatuchak Park rally site and assigned guards to inspect the scene.
He said the grenade was believed to be shot by M-79 launcher and fell at the MRT underground ventillation building inside Chatuchak Park where protesters were camping.
One protester was slightly hurt when some bomb fragments hit his arm and two cars were damaged, Mr Issara said.
He said the assailants were initially in a black pickup truck on the tollway and shot the grenade into the protester tents.
The attackers might have been in a hurry, causing the grenade to miss the target, the protest leader said.
Following the incident, the PDRC leaders cancelled their plan to lead protesters to seize the office of the Centre for Maintaining Peace and Order (CAPO), saying they feared for the safety of the protesters.