Majchrzak, ranked No. 76 in the world, produced an impressive display against Auger-Aliassime, the world No. 4 and a recent French Open quarterfinalist, Polish state news agency PAP reported.
It said the 30-year-old Pole did not lose serve during the match and committed significantly fewer errors than his opponent.
The victory on Friday was the biggest of Majchrzak's career and only the second time he has beaten a player ranked in the world's top 10.
Majchrzak will next face third-seeded Daniil Medvedev of Russia for a place in the final.
Earlier in the tournament, fellow Pole Hubert Hurkacz was eliminated in the first round after losing to Hungary's Marton Fucsovics 6-3, 6-7, 6-7.
Hurkacz also competed in the doubles. He and his Canadian partner Gabriel Diallo were knocked out in the quarterfinals on Friday, falling 6-7, 6-4, 7-10 to home favourites Sander Arends and David Pel.
The tournament in 's-Hertogenbosch is played on outdoor grass courts and serves as a warm-up for Wimbledon, which begins later this month.
(gs)
Source: IAR, PAP