Local residents have held protests demanding more jobs at the sites.
“Tullow confirms that there have been a number of demonstrations at Tullow operated sites in Northern Kenya today regarding local concerns around employment,” Tullow said in a statement.
“We have temporarily suspended our operations across Block 10BB and Block 13T in Turkana East and Turkana South sub-counties. The priority at the moment is to ensure the safety and security of our staff.”
Tullow operates both of the affected blocks and owns a 50 per cent stake in the assets, with Africa Oil holding the rest.
Both explorers have struck oil at the blocks and are in the process of determining its commercial viability.
Tullow would not comment on whether any of its staff had to be evacuated from the drilling sites, located in a remote part of the east African nation.
In July, Tullow, which is already producing oil in Ghana and awaiting government approval to do so in Uganda, estimated resource volumes in the Lokichar basin in Kenya's northwest at 300 million barrels of crude oil.
In addition to Kenya, oil discoveries in Uganda and gas finds offshore Tanzania and Mozambique have drawn explorers to east Africa, now seen as a potentially major new producing region.
Exploration director Angus McCoss said last month that the company is looking to increase the pace of exploration in Kenya and is aiming for 12 wells over the next 12 months.