The US Geological Survey said the quake was measured at a magnitude of 7.8 and at a depth of 10km.
It said a series of aftershocks followed, measuring up to 5.8.
Russia's emergencies ministry said the quake in the country's far east had a magnitude of 7.2.
Governor Vladimir Solodov said all emergency services had been placed in a state of high readiness, but no damage had been reported.
A tsunami warning was issued for the eastern shore of the peninsula, jutting far out into the Bering Sea and Pacific Ocean.
He said tsunami waves ranging from 0.5m to 1.5m were expected at various points along the coast and warned people to stay away from coastal areas.
"This morning is once again testing the resilience of Kamchatka residents," Solodov wrote on the Telegram messaging app.
"Immediately after the earthquake, we began a rapid inspection of social institutions and residential buildings."
A tsunami warning was also issued for parts of the Kuril island chain, north of Japan, the emergencies ministry said.
The US National Weather Service and Pacific Tsunami Warning Center issued a tsunami advisory for parts of Alaska following the quake, warning of strong currents, and a forecast of waves of up to 3m for parts of the Kamchatka coast.
Kamchatka is in a highly seismic area and at least two quakes with a magnitude greater than 7 have occurred in the past week.
