The law allows punishments up to 400 lashes for offenses including rape, the consumption of alcohol, homosexual sex and gambling.
The law replaced elements of Indonesia's criminal code with sharia, or Islamic law, for Muslims.
Married people would be penalized to death in case found guilty and unmarried people would be lashed 100 times.
However, to many this is a regressive law and goes against the secular basis of Indonesia.
"The laws that have been approved in Aceh are cruel and degrading to humanity," said National Commission on Human Rights (Komnas HAM) head Ifdhal Kasim.
Aceh had previously adopted a moderate form of sharia law in 2001.
Nearly 90 percent of Indonesia's 234 million people are Muslim.