The company said it laid off 440 workers, or almost half its work force.
Advantage said it will continue operating at its remaining locations during the bankruptcy, and is exploring strategic alternatives, including a possible sale or merger.
Rental car companies such as Advantage, Hertz Global Holdings Inc. and Avis Budget Group Inc. have been hurt by the slowing economy as customers cut their discretionary spending on travel, translating to lower rentals.
"We have been hit with a simultaneous drop in leisure travel, with greatly increased costs, and frozen credit markets," Advantage spokesman Jon Austin said in a statement on Monday.
The company and 14 affiliates filed for Chapter 11 bankruptcy protection in the U.S. Bankruptcy Court for Minnesota.
Advantage said it would immediately move to consolidate its retail network. The 21 locations it is closing would be open only for the return of vehicles and will not be renting additional vehicles. It also said it made arrangements with Hertz Car Rentals to honor nearly all of its pending reservations at locations it is closing.
In October, the company had said it ran about 50 U.S. locations and 36 affiliates internationally. It is privately held by Denny Hecker Family Ventures.
About 460 people are still employed at the company's other locations and its corporate headquarters in San Antonio, it said.