Normally municipal councils determine which children get places in schools based on a queue system.
But the new law makes it possible to set aside five percent of places in free schools for children who have been in Sweden for less than two years before the school year begins.
It will be voluntary for free schools to take this step, and possible after 1 November.
Education Minister Gustav Fridolin says there are hundreds of schools that do not take new refugees: "It is scandalous when we have the worst refugee catastrophe since the Second World War. Today it is free schools that want to accept them, but rules and regulations have made this difficult."
The new law is based on a cross-party agreement by the centre-left and centre-right parties. The Left Party, which opposes free schools, and the Sweden Democrats, who oppose a multicultural society, are not part of this compromise.
Sweden's "free schools" are privately run, often for profit, but receive public money and are regulated by municipal councils.