Fourth seed Wawrinka was set to play either Canadian second seed Milos Raonic or Ukrainian Sergiy Stakhovsky.
Wawrinka started out on fire in the opening set as he committed one error and fired at 100 percent on first serves on his way to defeating Müller for the second time this season.
Wawrinka matched Müller on serve, with nine apiece; he finished with 21 winners.
"It was a really close first set, but it was a very good match for me," said Wawrinka, who last played here in 2005.
"I'm getting better and better with each match," he said.
"There was nothing really wrong with my game, I think I did everything pretty well," Wawrinka said.
At the top of the draw, Frenchman Gilles Simon ended a 12-match losing streak to Scotland's Andy Murray as he dumped the top seed out in the quarterfinals.
The persistent challenger stood 1-12 against the two-time Grand Slam winner and unleashed one of his best performances to stage the 6-4, 6-2 upset.
Simon will take a 6-3 record into his semifinal with defending champion Tomas Berdych, who scraped his knuckles during a second-set fall on court on the way to a defeat of France's Gael Monfils 6-1, 6-4.
Murray, who went down double breaks at the start of each set, confessed to getting off to a poor start; the recent Australian Open finalist admitting he never found the rhythm to recover.
"I struggled with most shots and I had a poor start," said the world number four who won the Dutch title in 2009.
In other tennis news, Wawrinka and fellow countryman Roger Federer announced on Friday that they would not be playing for defending champion Switzerland in Davis Cup play against Belgium next month.
Both players issued statements citing busy calendars to explain why they were skipping the first round of the tournament set for March 6th-8th.
Wawrinka said it was a difficult decision after playing in 22 of 23 Davis Cup rounds for the Swiss team since 2005.