Under tight security, the couple tied the knot Saturday at an exclusive resort strewn with colorful lights and flower garlands.
On Monday afternoon, the newlyweds boarded a helicopter near Ranthambhore National Park and arrived in the city of Jaipur, where they took a chartered flight to the Maldives, Jaipur airport director R.K. Singh said. The nation of tiny coral islands in the Indian Ocean is renowned for its high-end resorts.
Friends who arrived by road joined the couple on the flight, Singh said.
Locals had mixed feelings about the celebrity visit, and Rajasthan state's chief minister on Monday ordered an investigation into public complaints about party noise that lasted into the early hours of Sunday, local district collector Ravi Kumar Surpur said. Local laws bar noise beyond 10 p.m. that would disturb local communities or wildlife.
The Ranthambhore National Park is home to tigers, leopards, wild boars and other animals. If laws were broken, the concerned parties or the resort management would be charged, Surpur said.
Also, two men from the wedding party apologized for assaulting four news photographers, including one from The Associated Press, then taking their car keys and stranding them in the wild tiger reserve Friday. The written apology acknowledged "physical assault" and "bad behavior."
Because of the apology, no formal police investigation was opened. None of the photographers sought medical care.
Local hoteliers and tour operators said the celebrity wedding brought positive attention to the tiger reserve.
The wedding "would only serve the cause of tiger conservation," local hotel owner Balendu Singh said. "The event was a big success, and Ranthambhore would get enough mileage as a tourist destination."
Brand, a 35-year-old British comedian and actor known for a drug-addled past and hedonistic tendencies, is next set to star as Trinculo in "The Tempest" and the title character in a remake of "Arthur."
Pop star Perry turned 26 on Monday. Her second album, "Teenage Dream," was one of this year's best-sellers.