Three men, all aged 25-30, are suspected of murder after the victim was stabbed in the throat.
Police declined to release the nationalities of the casualty or the three alleged attackers.
Two suspects were detained immediately after police arrived at the Storå asylum centre, located 200 kilometres west of Stockholm, and found the victim seriously wounded. He was taken to hospital where he died from his injuries at around 9.30am.
The third man ran into the woods but was later arrested when he turned himself over to the police in Lindesberg.
"We don't yet have any information about a motive," police spokesman Stefan Wickberg told the TT newswire.
The victim and his attackers all lived at the asylum centre, police said. Officers began questioning the suspects over the course of Friday morning.
"We now need to secure anything that can help us in terms of forensic evidence," said Wickberg.
"The second thing to do is gather information from various people. The third thing is to establish as accurately as possible who did what. Presumably they didn't all hold the same knife."
Police were alerted to the attack shortly after 5am.
"Asylum centres have been a problem for us and we have had frequent calls to sort out fights and other disturbances," Wickberg told AFP.
"People in these centres live too close together and many of them come from war zones. It's not easy for them to all get along," he added.
The deadly attack marked the third murder at a Swedish asylum centre this year.
Migration minister Morgan Johansson described the incident as “incredibly tragic” and said he was watching developments closely.
People living in homes for asylum seekers were in a precarious position, the minister said.
“Here we have people who have to wait a very long time while also finding themselves in a very frustrating situation,” he told TT.
“The have fled from a country and they're not getting any answers. Now, we don't know the background in this particular case but we have boosted security and doubled the number of guards at asylum centres.”
The minister added: “We maybe need to be prepared to do more but we need to remember that that we have 100,000 people in our asylum centres, and in the autumn we had to compress quite a lot, so people are living in cramped surroundings.”
The home near Lindesberg is made up of four apartment blocks, according to the Migration Agency, which is sending staff to the scene.
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“We'll be there to offer support to anyone who needs it over the weekend,” said agency spokeswoman Alexandra Elias.
In 2014, there were 148 incidents at asylum centres throughout Sweden and in 2015 that number jumped to 322.
Arson attacks targeting asylum shelters have also surged, with at least two dozen centres reduced to ashes or damaged by fire last year.
Sweden, like the rest of Europe, has been struggling with the continent's biggest migration crisis since World War II.
A country of 9.8 million, Sweden took in more than 160,000 asylum-seekers in 2015, putting it among the EU states with the highest proportion of refugees per capita.
It has since tightened its asylum rules to curb the migrant flow.