"We are still investigating the attack and its motive. We now have arrested three suspects whom we are questioning," said police spokesman Stefan Wickberg.
Police declined to release the nationalities of the casualty or the three suspects.
Arsonists attack another migrant centre in Sweden
Police were alerted to a fight at the Stora Asylum Centre outside of the town of Lindesberg, some 160 kilometers (100 miles) west of Stockholm, at about 5:15 am (0415 GMT) on Friday.
The victim was stabbed in the throat and rushed to hospital, but died shortly after his arrival, said police.
Two other murders have occurred at Swedish refugee centres this year.
"Asylum centres have been a problem for us and we have had frequent calls to sort out fights and other disturbances," said Wickberg.
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"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.
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.
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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.
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