"Qanun jinaya is part of the implementation of Islamic sharia in Aceh and it's been much anticipated by Acehnese who want to apply it in its entirety," majority Aceh Party spokesman Muhammad Harun said.
The law regulates affairs such as extramarital and homosexual sex, rape, sexual harassment, alcohol, gambling and mixing between unmarried men and women.
People caught having pre-marital, extra-marital or homosexual sex face up to 100 lashes of the cane, or a fine of one kilogram of gold, or 100 months in prison.
An unmarried couple caught kissing could be punished with 30 lashes, a fine of 300 grams of gold or a prison term of up to 30 months.
Ramli Sulaiman, chairman of an Aceh parliamentary commission that drafted the law, said proving extramarital and gay sex would be difficult.
"There must be clear evidence and four witnesses who saw the act themselves," he said.
"We can't just accuse people of having extramarital or homosexual sex."
The law also applies to non-Muslims, but they can choose to be punished under sharia law or secular national law, he said.
Amnesty International criticised the law as "an enormous step backwards for human rights".
"Laws that criminalise sex outside marriage violate the right to privacy and are used disproportionately to police and punish women's choices," said Richard Bennett, Amnesty's Asia-Pacific director.
"They also act as a deterrent to women reporting rape and sexual violence who may fear being accused of sex outside marriage."
Amnesty said at least 156 people have been caned in Aceh since 2010 for offences such as gambling, mixing with the opposite sex and selling food during the Ramadan fasting month.
Officials said canings are mainly intended to humiliate rather than hurt the offenders.
Aceh is the only Indonesian province allowed to impose sharia, as part of the central government's attempts to pacify a clamour for independence.
Jakarta signed a peace agreement with separatist rebels in 2005, ending decades of conflict that killed more than 15,000 people.
