Cairngorm Mountain Rescue Team (MRT) said they called to Fingers Ridge in the Coire an t-Sneachda area on Saturday morning.
One climber was found to have suffered a serious arm injury but the second "appears to be ok", said the MRT.
Rescuers were carrying the climbers to safety on stretchers. The team said they would be airlifted to hospital when they get below cloud level.
In a separate incident, the team was also called to help three walkers lost on Bynack Mor.
They said they were making their way off the munro after some "coaching" from the rescue team.
Two climbers have been rescued after falling in the Cairngorms.