“They’ve fallen down, either free fall or tumbled down a cliff wall, after the anchor which attached them to the cliff wall came undone,” said Erik Johansson, deputy officer of the Norrbotten police force, to the TT news agency on Sunday morning.
One of the two injured climbers made contact with police via mobile telephone.
No other climbers are known to have been on the climbing expedition.
Several hours later, mountaineering rescue services were able to rappell down to a rocky ledge where the wounded climbers were resting, and a police helicopter winched them up before taking them to hospital in Kiruna.
It is not yet known how severely the two climbers have been injured.
“What I heard from the doctors is that they have serious injuries but that they are conscious,” Johansson told TT later on Sunday.
With its 2,106 metres and located in Sweden’s far north, Kebnekaise is the country’s highest peak, and is a popular mountaineering spot.