The pop superstar sported a giant beehive hairdo modeled on the country's white, orange and green flag at a Friday news conference.
At another appearance, she had placed a giant black net bow on her hair.
Gaga said she had been dying to visit India.
The practice sessions for the inaugural Formula One Indian Grand Prix started Friday. The final race, at a track in the suburbs of the Indian capital, is on Sunday evening. Lady Gaga will perform at an after-party.
The Associated Press contributed to this report.