Hingis suffered torn ligaments in her right ankle Saturday in her semifinal loss to Lindsay Davenport in Germany and the Swiss star ceded her No. 1 ranking to another American, Jennifer Capriati.
Meanwhile, Tauziat, the fifth seed from France, scratched out her seventh victory in nine career encounters with Magdalena Maleeva of Bulgaria, 7-6 (7-3), 6-7 (6-8), 6-3, in a first-round match.
Hingis will undergo surgery Monday and will be sidelined six to eight weeks.
The 21-year-old stretched for a backhand passing shot in the third game of Saturday's match but lost her footing and fell on her back. After dropping that game to go down, 2-1, she had her ankle taped but was forced to stop two points later.
Hingis retired for only the second time in her career and first since the 1998 Grand Slam Cup semifinals against Patty Schnyder.
The world's top-ranked player for 209 weeks, Hingis had to defeat Davenport to remain on top for a 74th consecutive week. She also was looking to win her third straight Porsche Tennis Grand Prix title and fifth overall.
Tauziat is seeking her first title in 16 career appearances at Zurich. She lost in the final in 1991 and 1997. The French No. 2 won her eighth career title in June, when she took the DFS Classic grasscourt event in Birmingham, England.
In other first-round action Sunday, eighth seed Silvia Farina Elia of Italy cruised past Anke Huber of Germany, 6-2, 6-4. Iroda Tulyaganova of Uzbekistan coasted to a 6-4, 6-1 triumph over Lina Krasnoroutskaya of Russia.
Tauziat and Tulyaganova will square off in the second round.
Capriati, Davenport, No. 4 Jelena Dokic of Yugoslavia and No. 9 Sandrine Testud of France, who took Hingis' spot in the draw, received first-round byes.