Police said the staff member, named by Swedish media as Alexandra Mezher, was taken to hospital but died of her injuries.
Relatives described her as "an angel", telling Expressen: “It is so terrible. She was a person who wanted to do good,” according to a translation by Sky News.
“We have cried a lot. She was such a nice person, warm and happy.”
It was unclear whether she had been deliberately targeted during a fight between several teenagers at the accommodation in Mölndal, near Gothenburg.
The 15-year-old suspect was restrained by other asylum seekers and has been arrested on suspicion of murder.
Thomas Fuxborg, a spokesperson for Swedish police, described the aftermath of the fight in the shelter as “messy” with blood on the floor.
“The perpetrator had been overpowered by other residents, people were depressed and upset,“ he told the TT news agency.
The shelter houses around a dozen asylum seekers aged between 15 and 19, who are among the thousands of unaccompanied minors who have arrived in Europe without their families in the past year.
Amal Hassan, who works at the home, told the Göteborgs-Posten newspaper that she was shocked.
“Everyone who lives here is really nice,” she added. “There has never been any trouble before.”
Staffan Alexandersson, a social worker for the group running the shelter, described the attack as a ”horrible and tragic event” and said a crisis team had been sent in to support staff and residents.
“We regret what happened, and we're working right now in the crisis team to deal with both staff and children,” he told TT.
Sweden’s Prime Minister, Stefan Lofven, visited the shelter on Monday and expressed his sadness at the “terrible crime”.
“I believe that there are quite many people in Sweden who are very concerned that there may be more cases of this kind, when Sweden receives so many children and youths arriving alone,” he told Radio Sweden.
It came as Sweden’s police commissioner, Dan Eliasson, requested 4,100 additional officers and support staff to help fight terrorism, carry out migrant deportations and police asylum accommodations, The Local reported.
"We are forced to respond to many disturbances in asylum reception centres,” he told TT.
"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.”
Around 163,000 asylum applications were made last year in Sweden, which is one of the main destinations for refugees and migrants entering the EU.
Swedish Migration Agency data shows the number threats and violent incidents at refugee shelters have been rising with the number of arrivals.
In 2015 the figure was put at 322, while arson attacks, threats and hate crimes against refugees are also on the rise.
Border checks came into force earlier this month after Sweden was granted a temporary exception from the Schengen agreement, as efforts continued to slow the number of arrivals.
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