Graham Paterson, 60, runs Skye Hi Cuillin Mountain Guides with his wife Annie in the Carbost area in the west of the island.
He has not been seen since Thursday, when another climber saw him fall on Cuillin Ridge. Skye has been lashed by storms and gales with more forecast. Mr Paterson was understood to have gone on the hills by himself. Northern Constabulary said he was believed to be injured.
A spokesman said: "A report came in from a member of the public who saw the man fall at around 2.30pm yesterday.
"Police, RAF, mountain rescue teams from Skye and Kintail and Search and Rescue Dogs Association dogs are involved. Conditions in the area are worsening and the forecast is poor."
He added: "The man's family are being kept informed of the circumstances."
Despite the report of the fall, it is understood the witness had difficulty pinpointing the exact location of the accident.
Mr Paterson's website says that he has been guiding walks, scrambles and climbs on Skye and elsewhere in Scotland since 1995, and adds that his wife "shares Graham's enthusiasm for climbing on the Cuillin Ridge".