An 80-year-old woman and her 16-year-old grandson were found by rescuers in the city of Ishinomaki, in Miyagi prefecture.
Sumi Abe and her grandson Jin Abe were in the kitchen when the quake struck, but the grandson was able to reach food from the refrigerator.
The pair is being treated in hospital, but details of the condition are unknown.
Attempts were continuing Sunday to restore power to systems to cool the damaged and overheating reactors at the Fukushima nuclear plant.
Operatior Tepco (Tokyo Electric Power Company) backed away from plans for a venting of radioactive gas at one of the troubled reactors, saying that pressure inside has stabilised.
Meanwhile, Japan continues to detect abnormal levels of radiation in milk and spinach from areas around Fukushima.
In the first report of contaminated food outside of Japan, authorities in Taiwan say they found slight amounts of radiation in a shipment of fava beans.
Tsai Shu-chen of Taiwan's Food and Drug Administration told RFI that the amount of radiation was quite low, but officials decided to inform consumers anyway.
“It’s only 14 kilograms, and because this product complies with Taiwan’s regulations, it can be imported,” she said.
“However because of the public concern here, we decided to share this information.”
Japan’s 11 March earthquake is the country’s deadliest natural disaster since the 1923 Great Kanto Earthquake, which killed more than 142,000 people.
Some 360,000 people have been displaced from their homes and have taken shelter in evacuation facilities in 15 prefectures.