The unseeded Muchova will meet defending champion Iga Swiatek, who reached the final for the third time in four years with a 6-2 7-6 (9-7) win over Brazil's Beatriz Haddad Maia on Thursday.
Sabalenka, the Australian Open champion, would have taken over the top spot in the rankings by winning the title in Paris.
But she suffered a massive loss of nerve against an opponent clearly struggling with cramp towards the end of an epic encounter, but who won the final five games.
Sabalenka failed to convert her chance at 5-2 in the third set and bowed out to the gifted Czech, 7-6 (7-5) 6-7 (7-5) 7-5. It was her first defeat in 13 slam matches this year.
The last unseeded player left in the men's or women's draw, Muchova, 26, did not attempt to match Sabalenka's massive hitting power from the baseline.
Instead the Czech, who battled back from the mid-200s into the top 50 after an injury in 2021, opted for a lighter touch.
She sliced the ball to take the pace off, playing Sabalenka's backhand and hitting drop shots to force the tall Belarusian into the net.
Sabalenka, the biggest hitter in the women's game, could not use her fierce forehand at will and was clearly rattled.
She was broken as Muchova moved 5-4 up in the first set but the Czech wasted one set point on her serve and was broken straight back before bagging the set at the second opportunity in the tiebreaker.
The Belarusian was then broken at the start of the second set. The pair traded two breaks each in the second set before Sabalenka earned two set points in the tiebreaker.
She squandered the first with a double fault but showed no nerves on the next to level.
Sabalenka wasted four break points at 1-0 in the third but snatched the key break to move 4-2 clear but her serve deserted her as the match reached its conclusion after more than three hours.
After Muchova had saved a match point at 5-2 down, she launched her own comeback to win five straight games and reach her first grand slam final.
Swiatek also found it tough going against Haddad Maia. The world No.1 showed rare signs of frustrations but managed to hold it together when it mattered to prevail as the clock ticked past 9pm.
Haddad Maia, the No.14 seed, had played four consecutive three-set matches to fight her way to the semi-finals but she finally met her match in Swiatek, who battled through a thrilling tiebreaker to claim victory.
Swiatek is likely to be the overwhelming favourite in Saturday's final: she has reached it without losing a set and had dropped just 23 games in her six matches.
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