Tens of thousands of residents have been forced to leave their homes because of the leak.
Tokyo Electric Power Co. is set to start paying out the money April 28.
The company expects to pay about $600 million in compensation to families, but it will take about $24 billion to resolve the current problems at the plant.
Roughly 48,000 households living within about 19 miles of the crippled Fukushima Dai-ichi nuclear plant would be eligible for the payments, said Trade Ministry spokesman Hiroaki Wada.
The company is still struggling to stabilize the nuclear plant, which saw its cooling systems fail after a magnitude 9.0 earthquake on March 11 triggered a massive tsunami that wrecked emergency backup systems as well as much of the plant's regular equipment.
Radiation leaks from the crisis have contaminated crops and left fishermen in the region unable to sell their catches, a huge blow to an area heavily dependent on fishing and farming.
The Associated Press contributed to this report.