Police fired tear gas to quell rock-throwing protesters who gathered outside the legislative council building in Kendari, the capital of South-east Sulawesi on Thursday.
One student died of a bullet wound during the violence, authorities said.
“This morning, another student, who was critically injured, died because of bleeding in the head,” the chief provincial ombusdman, Mastri Susilo, told dpa.
This week tens of thousands of students across the country have been holding daily protests, which have often turned violent, against revisions to the criminal code which include the criminalisation of sex outside marriage, co-habitation and insulting the president.
The violence in Kendari followed clashes on Tuesday in Jakarta that left more than 260 students and 39 police injured as security personnel and protesters faced each other outside the national parliament building, police said.
The proposed changes to the criminal code would see consensual sex outside of marriage punishable by up to one year in prison, while a couple living together without being married could be jailed for up to six months.
Anyone who insults the president or vice president could be handed a prison term of up to four-and-a-half years.
This was decriminalised by the Constitutional Court in 2016 after a legal challenge by citizens.
The protesters also demanded the government revoke recent revisions to a law governing the country’s anti-corruption commission that activists warn could severely threaten the body’s independence.