Seeded 13th, Mirza and her Belgian partner lost their third round match 2-6 4-6 to third seed rivals in 71 minutes.
Martina Hingis became world number one in 1997, at the age of 16, and won her first Australian Open, Wimbledon and US Open singles titles that year.
Sania Mirza advanced to the third round of both the women's doubles and mixed doubles events, while Rohan Bopanna and Purav Raja also won their respective mixed doubles matches.
Dan Evans was suspended after admitting last Friday he had failed the test at the Barcelona Open in April.
British world number 50 Dan Evans has been provisionally suspended after testing positive for cocaine.
French Open 2017: Jelena Ostapenko's Roland Garros victory signals arrival of next generation of stars
Jelena Ostapenko, the lowest-ranked Roland Garros champion in tournament history, bludgeoned her way to the title in a manner much befitting her idol, Serena Williams.
Bethanie Mattek-Sands and Lucie Safarova beat unseeded Ashleigh Barty and Casey Dellacqua of Australia 6-2, 6-1 for their third successive major title.
With five Indians in the main draw of French Open 2017, take a look at their form, partners and draws.
Presently ranked 52 in the world, Paes' last Grand Slam title in the men's doubles event came in 2013 with Radek Stepanek at the US Open.
Swiss Timea Bacsinszky beat Aryna Sabalenka of Belarus in straight sets to pull the scores level at 1-1 in the Fed Cup semi-final on Saturday.
Martina Hingis looks to reach a first Fed Cup final in almost two decades when Switzerland face Belarus with the former world number one revelling in her role as the team's "big sister".
Indian tennis star Sania Mirza on Saturday said she has had a "solid year already" and hopes to build on it with her new women's doubles partner – Yaroslava Shvedova of Kazakhstan.
Sania Mirza and her partner Barbora Strycova fought off a strong challenge from Martina Hingis and Chan Yung-Jan to reach the women's double final at the Miami Open tennis tournament.
Sania Mirza has allegedly evaded tax on the amount of Rs 1 crore that she received after becoming Telangana's brand ambassador.
Sania Mirza will have to wait for her seventh Grand Slam trophy as the Indian and her Croatian partner Ivan Dodig lost the Australian Open mixed doubles final 2-6 4-6 to underdogs Abigail Spears and Juan Sebastian Cabal, in Melbourne on Sunday.
Indian tennis ace Leander Paes and his Swiss partner Martina Hingis crashed out of the mixed doubles competition of the Australian Open with a straight-set defeat in the quarterfinals in Melbourne on Thursday.
Leander Paes and Martina Hingis don’t have the left and right hand combination of the Bryan Brothers, but they do have twin-esqe coordination. They don’t have a male player with the biggest serve, in a format that cashes in heavily on having one. So what is it about this pair that makes you want to sit up and watch them?
Sania Mirza and Rohan Bopanna set up a mixed doubles quarterfinal clash against each other at the Australian Open after winning their respective matches, in Melbourne on Tuesday.
Paes and Martina beat Australians Casey Dellacqua and Matt Reid 6-2, 6-3 in a second round match at Melbourne Park in 54 minutes.
India had a mixed outing at the Australian Open as Leander Paes got off to a winning start in mixed doubles but fourth seeds Sania Mirza and her partner's campaign in women's doubles ended with a loss to an unseeded pair on Sunday.