An Explosive Ordnance Disposal (EOD) unit was dispatched to the car park of a private bus operator in the Buddhamonthon area, next to the home of Mr Suthep, leader of the People's Democratic Reform Committee (PDRC).
Two unexploded M79 rifle grenades were found. Police believe they were fired from the nearby Baromratchchonnanee Bridge or the Buddhamonthon Sai 2 Bridge.
The bomb squad destroyed the grenades although they failed to function, saying that a delayed explosion was possible even though they had failed to detonate.
Mr Suthep shrugged off the incident, saying it took place on Saturday night, and that the grenades landed 30 metres away from his house.
Meanwhile, PDRC spokesperson Akanat Promphan told reporters that the property belongs to his mother Srisakhun Promphan who is also Mr Suthep's wife.
There was no one there at the time of the incident.