The small coastal town is currently experiencing its biggest influx of refugees to date, with several thousand people turning up every week since the start of September, according to authorities.
But out of 1,900 children who have arrived in Trelleborg over the last month without parents or older relatives, at least half are believed to have left the area without alerting officials, despite being given temporary accommodation there.
"We don't know where they are (...) We don't have the possibility to stop them leaving. We can't wait by their beds day and night," Agneta Sjölund, Director of Trelleborg Municipality, told The Local.
Sjölund said that most of the refugees had arrived in southern Sweden via ferries from Germany and had been registered in the town but not yet had their paperwork processed by Sweden's Migration Agency (Migrationsverket), which made it more difficult to keep track of them.
"Trelleborg has become a transit destination in a short space of time," added the director.
"With Migrationsverket...it's a slow process," she said.
Under the EU's Dublin Regulation, the European country in which an asylum seeker first arrives should take responsibility for the person. But Sjölund said that the municipality had received evidence to suggest that some of the missing children had moved on to Norway or Finland as well as other Swedish cities.
Earlier this week Cecilia Lejon, a labour market specialist for Trelleborg municipality who is also tasked with helping new arrivals integrate into the community told Swedish newspaper Sydsvenskan that she believed there were three major reasons that the children had left the area.
Alongside viewing Sweden as a "country of transit", she suggested that some "have friends and relatives elsewhere in Sweden and want to get there", while others "have absolutely no confidence in the authorities".
Trelleborg is the southernmost town in Sweden and has a population of around 43,000. It is situated around 30 kilometres from Malmö, Sweden's third largest city and a major hub for asylum seekers.
Migrationsverket was not immediately available for comment on the missing children.
Sweden is the most popular destination in Europe for unaccompanied minors. Almost a third of the 25,000 children who arrived in Europe without older family members in 2014 turned up in the Nordic nation, according to figures from Migrationsverket.
In July this year the government agency revealed to newspaper Dagens Nyheter (DN) that it had seen numbers soar by 93 percent in 2015 compared with the first six months of last year.
Meanwhile record numbers of people of all ages are continuing to seek asylum in municipalities across Sweden.
Earlier this week Migrationsverket revealed that a total of 86,223 people had launched cases so far in 2015, surpassing a previous record set in 1992 when 84,016 people asked for asylum following fighting in the Balkans.
Sweden's Prime Minister Stefan Löfven has raised concerns about a shortage of accommodation for the new arrivals, suggesting that tent camps may even be needed in order to provide enough shelter for people reaching Sweden as the winter sets in.