Servette's owner, Iranian businessman Majid Pishyar, said he had taken the decision with a "broken heart" and would continue to fight for the club.
The 17-times Swiss champions returned to the top flight of Swiss football this season after being declared bankrupt in 2005, when they were demoted to the third tier.
"The last few weeks have been very difficult for all those who love Servette," said Pishyar in a statement on the club's website.
"We have made every effort to ensure the future of the club. But, I have had to take a very difficult decision and have decided, with a broken heart, to file for bankruptcy. However, we will continue to fight for Servette."
Pishyar complained of a lack of local support for the club.
"I have invited all the partners to take part in the success of the club. To my great sadness, only a minority have joined us. I thank them from the bottom of my heart."
The Swiss Football League (SFL) said no decision had been made on Servette's future in the competition but that Saturday's match against FC Thun would go ahead. The team are fourth in the table.
Neuchatel Xamax were expelled from the league in January over what the SFL said were a number of irregularities including the suspicion that Russian-born owner Bulat Chagaev had forged a letter from a bank which he used as a financial guarantee.
Chagaev, who was subsequently arrested and who is currently in custody on charges of financial mismanagement, took the club over eight months earlier.
Sion were deducted 36 points for fielding players they club had signed while subject to a transfer ban.
The club then took their case to a civil court, defying FIFA and UEFA statutes, and Switzerland was threatened with an international ban.
