Police Scotland said the emergency services were alerted to the incident at about 13:00.
A coastguard helicopter and lifeboat joined rescue teams looking for the man.
A post on the RNLI Montrose Lifeboat Facebook page said it had been stood down at 18:20 "due to failing light".
A major search is under way for a man believed to have fallen from cliffs at Arbroath in Angus.