This marked Stokowski's second medal of the competition, after the bronze he earned in the men's 4x100m freestyle relay the previous day.
Stokowski clocked a time of 49.16 seconds in Wednesday's final, setting a new national record for the 100m backstroke in a 25-metre pool.
Russia's Miron Lifincev claimed gold with a time of 48.76, while Hungary's Hubert Kos took silver at 48.79, Polish state news agency PAP reported.
The 2024 World Short-Course Swimming Championships in Budapest run until Sunday.
Poland won two medals, a silver and a bronze, at the 2022 World Short-Course Swimming Championships in Melbourne, Australia.
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Source: IAR, PAP