The Pole, ranked No. 69 in the world, gave in to Gauff 1-6, 2-6.
She previously beat Russia's 190-ranked Anastasia Zakharova 4-6, 7-5, 6-4 in Round 3 (Round of 32) on Friday.
It's the first time she has reached the last 16 of a Grand Slam event.
Poland's world No. 1 Iga Świątek also dropped out of the tournament after being beaten by Linda Noskova of the Czech Republic 6-3, 3-6, 4-6 in Round 3 at the hard courts of Melbourne Park.
Meanwhile, the 9-ranked Hubert Hurkacz is to face France's Arthur Cazaux in round 4 on Monday.
Poland's Athlete of the Year Świątek reached the semi-finals of Australian Open in 2022.
The 2024 Australian Open, the first Grand Slam tournament of the year, runs on the hard courts of Melbourne Park until January 28.
Source: polskieradio24.pl, WTA