The adventurer and explorer, who turned 66 Sunday, said he fell asleep at the wheel on the A6 motorway in Greater Manchester and lost control of his Jaguar which veered across lanes headlong into a Nissan Micra just before 2 p.m. Saturday.
The Jaguar then hit a Ford Focus before finally stopping, The Daily Mail reported Monday.
The driver of the Nissan was seriously injured and a 5-year-old boy had minor head injuries, the newspaper said.
Fiennes was breath-tested as a routine matter and was not found to be drunk. Fiennes, who had a heart attack seven years ago, was taken to a hospital and checked out after complaining of shock and an irregular heartbeat.
The oldest Briton to conquer Mount Everest, Fiennes is described by the Guinness Book of World Records as the "greatest living explorer," the Mail said.
Falling asleep at the wheel is classified as dangerous driving in Britain and can be punishable with maximum two-year jail sentence or a fine.
Fiennes is a third cousin of actors Joseph and Ralph Fiennes.