The Pole won the 500m event at the Gangneung Ice Arena on Monday, Polish Radio's polskieradio24.pl website reported.
Falkowska clocked a time of 44.314 sec., topping the race ahead of South Korea's Minji Kang and Jaehee Chung, according to officials.
Another Polish speedskater Kornelia Woźniak came fourth.
Falkowska told reporters she had hoped to win a medal, but winning the gold came as a "big surprise."
It is the second medal for Team Poland at the 2024 Winter Youth Olympic Games, after Łukasz Łukaszczyk scooped the bronze in men's ski jumping, Polish Radio reported.
The 2024 Winter Youth Olympic Games in Gangwon run until February 1.
Source: IAR, polskieradio24.pl