Kaczmarek finished second in Wednesday's final, with a time of 49.57 seconds, the third-best time of her career, Polish state news agency PAP reported.
Marileidy Paulino of the Dominican Republic claimed the title, with 48.76 seconds, while Sada Williams of Barbados took the bronze after finishing in 49.60.
Poland's first medal at the championships in Hungary came from Olympic champion Wojciech Nowicki, who finished second in the men's hammer throw on Sunday.
Poland's track-and-field federation has selected a team of 67 athletes to compete for medals at the 2023 World Athletics Championships, which run in Budapest until August 27.
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Source: TVP, IAR, PAP