The ministry said that there may be no connection between the two and that another five people who were vaccinated from the same vial as the man who died are in a satisfactory condition.
It said that under Ukrainian law and international standards for the organization of pharmacovigilance for adverse events after immunization, every death that occurs within 30 days of immunization must be investigated.
Pfizer was not immediately available for comment from its office in Ukraine outside of normal business hours.
About 2 million people in Ukraine have received their first shot since February, but no deaths caused by vaccination have been reported.
Ukraine, with a population of 41 million, has been among the European countries most affected by the pandemic, with around 2.24 million COVID-19 cases and 52,460 deaths as of July 3.