The magazine was sold briskly at stalls across the capital on Friday.
Protesters hit Indonesian streets when the magazine announced in January it was planning a local version, but it remains to be seen whether demonstrations will pick up again after people have read it.
One hard line group, the Islamic Defenders Front, pledged to forcefully remove the magazines from shops.
Tubagus Muhamad Sidik, the group spokesman, said: "The first edition might be tame, but it will get more vulgar. Even if it had no pictures of women in it, we would still protest it because of the name."
Muslim leader Yusuf Hasyim said the magazine posed more of a threat to Indonesia than terrorism by al-Qaeda-linked militants who have killed more than 240 people across Indonesia in recent years.
"This is a kind of moral terrorism that destroys the way of the life of the nation in a systematic and long-term way," state news agency Antara quoted Yusuf Hasyim as saying.
"Let the people look at it and see what they think, hopefully they will accept it"
Playboy promotion manager
He went on to urge Muslim youths not to attack shops selling the magazine but to express their objections peacefully.
Playboy, which already has 17 international editions with content tailored to local tastes, played down the protest threats.
The Indonesian version costs about $5, more than twice the minimum daily wage in Jakarta, but affordable to many middle- and upper-class city dwellers.
The magazine has drawn protests
from Islamic groups
"Let the people look at it and see what they think, hopefully they will accept it," said promotion manager Avianto Nugroho.
"If there are demonstrations, we will try to meet their demands."
Most Indonesians practice a moderate form of Islam, and many women shun standard Middle Eastern forms of dress associated with Muslims.
Many Indonesian women do not cover their heads and often dress in tight-fitting jeans and sleeveless tops.
Indonesian versions of Western magazines FHM and Maxim, which also contain photos of women in underwear, are already on sale.
Local tabloids feature more explicit photos and stories and pornographic VCDs, though illegal, are sold more or less openly at markets all over the country.