Sabuni, a member of parliament and a board member of the Liberal Party, quoted a study from Stockholm University which claims that 100,000 girls and young women live under so-called 'honour oppression' in Sweden.
Writing in Expressen, Sabuni said that all public funding should be withdrawn from religious schools, as they could not guarantee to respect children's right to equality.
Introducing compulsory gynaelogical checks would reveal when girls have been subjected to circumcision, or genital mutilation. Such checks should be part of the medical checks given to all Swedish schoolchildren during high school, Sabuni argues.
"Such examinations not only function as checks, but also give an opportunity to discuss sexuality, women's private parts and typical female diseases," she writes.
On the question of headscarves, Sabuni says that they should not be allowed until girls are at least 15.
"The Prophet himself is supposed to have said that girls should first hide themselves when they start puberty. Today girls are already wearing headscarves in nursery school."
"We need to tear down the foundations that honour culture lies on in Sweden," writes Sabuni. She wants to introduce the term 'honour-related violence' into Sweden's penal code, make it possible to launch prosecutions for female circumcision even many years after the crime was committed, and to forbid doctors from providing 'virginity certificates'.
Other proposals put forward by Sabuni include criminalizing child marriage and forced marriage, and imposing limits on dowries.
"The government's 'investment' of 180 million kronor to strengthen efforts to combat honour-related violence is not having the desired effect," Sabuni writes.
"Local municipalities that were expected to initiate projects and match central government's investments have shown no great interest," she adds.