The health and labour ministry said the man has received government approval for compensation for the radiation-induced illness.
He helped install covers on damaged reactors at the plant from October 2012 to December 2013.
He did not work at Fukushima in the weeks after the massive earthquake and tsunami destroyed the plant in March 2011.
The man had worked at several other nuclear plants before landing at the Fukushima plant, the ministry said.
Medical experts could not determine whether his exposure at Fukushima was the direct cause of his leukaemia, a ministry official said.
But his total exposure of 19.8 millisieverts was mostly from his work at Fukushima, the official said.
Thirteen other workers in Japan’s nuclear industry have been certified for government compensation for cancer and other illnesses linked to their radiation exposure since the 1970s, according to the ministry.
Since the Fukushima crisis, 10 compensation cases have been filed, with seven being rejected and three still being examined.
A claimant can be considered for compensation for illnesses linked to radiation exposure with annual dose exceeding 5 millisieverts and the illness developing more than a year since first contact to radiation.
Since the crisis, nearly 45,000 workers have worked at Fukushima, about half of them with exposure levels exceeding 5 millisieverts.