The 'Poker Face' hitmaker is accused of disrespecting the nation by tying the ensign to a motorbike and riding the vehicle across the stage while wearing a provocative outfit, reported Sun online.
"Not appropriate and hurt the feelings of the Thai people," said the ministry.
The ministry's Permanent Secretary Somchai Seanglai confirmed that they do not intend to seek legal action against the 26-year-old singer.
Gaga's Asian tour has been marred with controversy, and a concert in Indonesia was axed following complaints that it breached obscenity laws.