"The secretary is not feeling well after a long couple days working on major issues back home such as North Korea," the state department said.
Mr Tillerson, on his first official trip to Africa as Washington's top diplomat, is in Kenya until Monday.
The news came a day after US President Trump shocked the world, agreeing to meet North Korea's Kim Jong-un by May.
Officials accompanying Mr Tillerson, 65, on his five-nation tour of Africa did not specify his illness but it is understood not to be serious.
Mr Tillerson was in the Ethiopian capital of Addis Ababa when news of Donald Trump's agreement to meet Mr Kim in unprecedented talks broke late on Thursday.
The decision is reported to have been taken without consultation with key advisers, including Mr Tillerson.
The top US envoy had told reporters just hours before the surprise announcement that Washington was "a long way" from talking directly to North Korea.
The US secretary of state has been on the road for four days, visiting Ethiopia, Djibouti and Kenya. He is scheduled to go on to Nigeria and Chad.
"Some events will go ahead without him, while they are looking at the possibility of rescheduling others," spokesperson Steve Goldstein told reporters travelling with Mr Tillerson.
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