The 14th-seeded Osaka, who knocked out world No. 1-ranked Aryna Sabalenka in the previous round, entered the day as the only player in the men's or women's draw who had yet to drop a set.
After being broken twice in 37 games over her first four matches, Osaka was broken twice in the first set alone. She committed four double faults and had 32 unforced errors for the match, both her most this tournament.
"It's hard for me to immediately think of something positive. I feel like it's hard because I played so well in my last match, then today I just feel like I didn't play well at all and I didn't have any energy," Osaka said.
It was a rematch of the Bad Homburg final, which Muchova won after Osaka retired in the second set with a foot injury. Before this year, Muchova hadn't won a title since Seoul in 2019, which was the first of her career. She won the WTA 1000 event in Doha in February and then Bad Homburg, a grass-court tuneup event for Wimbledon.
The Czech, 29, has won nine straight matches -- all on grass -- dating to the start of that Bad Homburg title run, which breaks a tie for the longest tour-level win streak of her career (previous was eight straight earlier this year spanning her Doha title and Indian Wells).
"It's unbelievable -- I'm super happy with today's win," Muchova said in her interview from No. 1 Court. "I played three times on this court and it was 0-3. I had a not good relationship with this court, but I am super happy we finally made it and I got the win."
Osaka fell to 5-1 in Grand Slam quarterfinal matches; only Chris Evert (48) and Sabalenka (eight) had longer win streaks in major quarters to start their careers.
Muchova, the 2023 French Open runner-up, has now reached the semifinal round at all four majors. Entering the day, she was 0-2 in previous Wimbledon quarterfinal matches, in 2021 and 2019.
She will play seventh-seeded American Coco Gauff on Thursday for a spot in Saturday's final. Gauff leads 6-1 in their tour-level matches, though Muchova won their most recent meeting in Stuttgart in April.