Lady Gaga wore a traditional Thai headdress and a bikini and sat on a motorcycle with a Thai flag tied to it.
The ministry says the act was "not appropriate and hurt the feelings of the Thai people."
The ministry's Permanent Secretary Somchai Seanglai says his agency gave police a summary of public complaints it received.
Somchai says that is protocol but the ministry does not intend to seek legal action against the American pop diva.
Her Asian tour has been wildly popular but also raised objections. An Indonesian show was canceled after Muslim hard-liners denounced it.