The woman was vaccinated on Friday and is suspected to have suffered a brain hemorrhage three days later, on Monday, it said. It was Japan's first reported death following a vaccination.
"The brain hemorrhage that is suspected as a cause is relatively common among people from their 40s to their 60s, and at this time, based on examples overseas, there does not seem to be a link between brain hemorrhages and the coronavirus vaccine," the ministry quoted Tomohiro Morio, a doctor advising the government, as saying.
"It may be a coincidental case, but there is a need to gather more information and make an assessment in upcoming working groups."
Global health authorities have praised the fast development of safe and effective COVID vaccines, but have warned people with serious underlying health conditions to take medical advice first.
Japan became the last member of the Group of Seven leading industrialized nations to begin its vaccination drive, on Feb. 17.
It has so far received three shipments of vaccine developed by Pfizer and BioNTech.
Japan officially approved Pfizer's vaccine last month, the first such approval in the country as it steps up efforts to tame infections in the run-up to the Summer Olympics.