The database was released in 2016 and was built of online images of 100,000 well-known people.
The database is believed to have been used to train a system operated by police forces and the military.
The deletion comes after Microsoft called on US politicians to do a better job of regulating recognition systems.
Microsoft told the FT the database was no longer available, because the person who curated it had now left the company.
Last year Microsoft President Brad Smith asked the US Congress to take on the task of regulating the use of facial recognition systems because they had "broad societal ramifications and potential for abuse".