It's an interactive game where people pay money to enter a room where they must solve puzzles and riddles in a race against the clock to escape from the locked room.
The 15-year-old girl would be celebrated on the Friday in the recreational facility in the North of Poland, Koszalin birthday, said interior Minister Joachim Brudzinski of the private television channel TVN24.
The cause of the fire is not yet known, but officials are carrying out safety checks on every escape room in Poland.
Images from the scene show several emergency vehicles outside a building with a large "escape room" sign in front.
The five girls who died, all 15, were celebrating a friend's birthday when they visited the attraction.
In a follow-up tweet he demanded that the cause of the fire "must be fully explained".
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A 25-year-old man with severe burns was taken to an intensive care unit.
Since Friday, more than 200 of Poland's 1100 escape rooms have been checked, revealing a number of safety flaws that needed to be immediately fixed.
The move comes as prosecutors presented charges against the man who designed the entertainment site - identified only as Milosz S - with intentionally creating a fire danger and unintentionally causing the deaths of the girls in the city of Koszalin. According to initial findings, the fire brigade, the fire broke out in an adjoining room.
Koszalin Mayor Piotr Jedlinski announced that Sunday would a day of mourning in the city.
President Andrzej Duda tweeted a message of support to the families of the victims, calling it a "devastating tragedy".
Mr Brudziński insisted fire safety controls would be enforced in all escape room across the Eastern European nation. The game is in the last few years in many countries becoming more and more popular.