Heng suffered a stroke in 2016, raising questions about his long-term health.
“I know that the top job imposes exceptional demands on the office holder,” he wrote. “While I am in good health today, it is in the best interests of the nation for someone who is younger to tackle the huge challenges ahead.”
Prime Minister Lee said in a separate letter that he understands and respects the decision.
Heng will stay on as deputy prime minister, but will relinquish his finance minister post in the next Cabinet reshuffle, Lee said. The reshuffle is expected in about two weeks.