Board spokesman Ruben Ahlvin told the Swedish news agency TT that new regulations have made it harder for families separated as refugees to be reunited in Sweden.
Sweden has worked for many years with UN agencies to take in specific numbers and types of refugees, from refugee camps, in addition to asylum applications received in Sweden.
But under a tightening of existing legislation, applicants to the quota scheme will no longer be able to apply for asylum on behalf of family members from whom they have become separated.
Now those family members will have to apply for asylum themselves to Swedish embassies.
Sweden is set to take in some 1,900 asylum seekers under the quota scheme this year, many from Iraq, Uzbekistan and African countries, that do not have Swedish embassies.
The board says it fears the new rules are likely to hit small children and young women, who are particularly at risk of abuse once a politically active family member seeks asylum.