More than 1,800 athletes from 46 Muslim-populated countries are taking part in the games in the world's most populous Muslim country, organisers said.
"Let's put aside our political burden," Indonesian President Susilo Bambang Yudhoyono said in the opening ceremony, as he paid particular tribute to the Egyptian, Syrian and Palestinian delegations attending the event.
"Through this event, let's prove to the world that Islamic countries can live in unity and harmony," he said.
The opening ceremony in Palembang, a city on Sumatra island, was modest, reflecting the lack of funding for the event.
Local organisers said they had yet to receive any cash from the central government.
"It's scary. The funding has not been disbursed until now, we are asking left and right for support so the event can go ahead as planned," Djoko Pramono, a senior organising committee member, told AFP.
The event, which will continue until October 1, has faced a string of other problems including two changes of venue.
It was moved from Riau in Sumatra to the capital Jakarta, only to be shifted to Palembang after Sumatran officials complained.
Organisers had less than two months to move everything to the new venue.
The games were first held last year in Saudi Arabia, where bikinis were banned, men and women had to compete on separate days and men were barred from watching women swim.
However, the Indonesian organisers have ruled out such restrictions. They also rejected requests by some countries to stage male and female events on separate days.
"We have said since last year that we are going to follow international rules, not Muslim rules," Pramono said.
"We are giving the athletes the full freedom to wear whatever they want. If they want to wear the burqa or headscarf for beach volley, please go ahead, we will not ban them," Pramono added.
Rita Subowo, the head of Indonesia's Olympics Committee, told AFP that the Indonesian beach volleyball team would wear two-piece costumes for ease of movement and because such outfits were approved by the International Olympic Committee.
The games started with basketball and soccer, and 11 other sports will begin in the coming days.
Eyebrows have been raised over the Palembang complex itself, where parts of the ill-fated 2011 Southeast Asian Games took place.
Some facilities were not fully constructed when the 2011 event opened and scores of athletes suffered food poisoning there.
During the 2011 games two football fans were crushed to death in a stampede at a venue.
But Pramono remained optimistic about the Islamic games, which bring together member nations from the Organisation of the Islamic Conference.
