Leader Master Jinje of the Jogeye order said he would "self-repent" on behalf of the monks, the BBC reported.
Six monks offered to resign because of the incident.
A tape on television showed monks apparently playing poker, with some drinking and smoking.
Gambling is illegal in South Korea outside designated facilities, such as casinos. Gambling also violates the Jogye order's code of conduct.
The order, which says its followers make up about 20 percent of South Korea's population, has been hit by factional infighting, the British broadcaster said.
Local media reports said the video was thought to have been shot by a Jogye monk who was characterized as an opponent of the current administration.