A 25-year-old man has been hospitalized with burns and could not be immediately questioned by investigators.
The group was celebrating a birthday on Friday.
Autopsies showed the girls died of carbon monoxide asphyxiation, prosecutors said, a technical term for smoke inhalation.
In the United Kingdom, the number of escape rooms has soared from just seven in 2013 to more than 1,000 as of a year ago.
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Last night, four of the five victims were named on local news websites and social media as Karolina Barabas, Gosia Tymieniecka, Wiktoria Julia Pietras and Amelia Wieczorek. Regarded as an intellectual challenge, the games are highly popular among teenagers in Poland. The bodies were found locked inside a room where players must find clues to get themselves out.
Police at the scene of the fire tragedy in northern Poland.
Two hours after the tragedy, interior minister Joachim Brudzinski ordered the commander of the State Fire Service to inspect emergency exits in all similar escape rooms, which will start tomorrow.
The horrific incident happened in a residential building with an escape room inside.
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Ryszard Gasiorowski said the suspect, identified only as Milosz S, had neglected to ensure escape routes that could have allowed the girls to flee during the blaze.
Poland's Prime Minister Mateusz Morawiecki vowed earlier on Sunday to close escape rooms that fail to meet safety standards after firefighters inspected almost 200 such facilities across Poland over the weekend.
Prime Minister Mateusz Morawiecki, along with Suski and Szymczyk, spoke after holding a meeting in which they discussed with other officials ways of improving safety at entertainment venues.
Poland's President Andrzej Duda sent his condolences to the victims' families on Twitter.
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