Sindhu pocketed the first game 21-18 and the second game was level 1-1 before the Indian felt discomfort on her left knee.
It turned out to be a forgettable day for the Indian squad as both stars went down in straight games.
The 31-year-old former Wimbledon and French Open champion had been provisionally suspended since October 2022 after testing positive for banned blood-booster roxadustat at the US Open last year
The Serbian defeated Casper Ruud of Norway, 7-6(1) 6-3 7-5 in the final.
The Pole, who had not dropped a set in the tournament, was 4-1 up in the second before Muchova won four games in a row and forced a decider.
He has made it to the French Open final for the second year running.
Alcaraz suffered an injury after levelling the match 1-1 in the semifinals.
The defending champions defeated the Brazilian 6-2, 7-6(7) to set up the title match with Karolina Muchova.
The Czech is only the third player ranked outside the top-40 to reach the final at Roland Garros.
Sixth-seed Rune, who had beaten Ruud at the Italian Open last month, littered the court with 26 unforced errors in the first two sets.