Deputies adopted a proposal from the centre-right government, which said that in “normal circumstances” the Swedish contingent would be around 70.
The Swedish military will also provide materiel to the UN mission.
“Armed extremist groups and criminal groups have since the beginning of 2012 committed extensive acts of cruelty which have caused great human suffering in Mali,” parliament wrote in a statement, saying this justified the UN mission.
Parliament approved a maximum cost of 85 million kronor ($13 million) for the Swedish effort.
The UN force being deployed in Mali, known under the acronym MINUSMA, is to take over security duties from French forces who entered Mali in January to halt an Islamist advance and help the government re-establish its authority over the vast country.
The UN Security Council in April approved the force for Mali, to be made up of 12,600 international troops and police to take over from French and African forces.
Rwandan General Jean-Bosco Kazura has been appointed to command the force.