The 22-year-old victim was rushed to a nearby hospital but died of her wounds, police said.
Police would not comment on the identity or nationality of the alleged attacker, except to say that he was a young man who was a resident of the centre for 14- to 17-year-olds.
He was under arrest for murder.
‘These kinds of calls are becoming more and more common. We're dealing with more incidents like these since the arrival of so many more refugees from abroad,’ police spokesman Thomas Fuxborg said.
The attack came as National Police Commissioner Dan Eliasson on Monday requested 4,100 additional officers and support staff to help fight terrorism, carry out migrant deportations and police asylum accommodations.
‘We are forced to respond to many disturbances in asylum reception centres. In some places, this takes significant police resources. This was not the case six months ago and it means that we won't be able to respond as effectively in other areas,’ Eliasson told Swedish news agency TT.
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, which put 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.
