The referendum was launched by opponents of the law who managed to collect the 80,000 signatures needed.
The referendum results will be announced Sunday. If Slovenia confirms the law, it would become the first central European country to do so.
The President of Slovenia, Borut Pahor, supported the law at first, but in recent weeks, he adopted a low profile while waiting for the results.
Dušan Vučko, a spokesperson for the Slovenian electoral commission, told Delo that a minimum of 343,104 voters (20% more than 1.7 million registered) will have to cast their vote for the result of the referendum to be valid. More than half of those who vote will need to reject the law in order for it to be overturned.
In 2012, in another referendum, voters rejected by 54.55% a bill that would have expanded rights for same-sex registered partnerships.
However, surveys have shown since that the support of the law has grown, but is still very close between those who support and those who oppose equal marriage.