Niki, whose roughly 20 planes serve resorts in southern Europe and north Africa, ceased operations late on Wednesday after applying to open insolvency proceedings.
This followed an announcement by Germany's Lufthansa that it was no longer interested in buying Niki together with the rest of Air Berlin because of EU competition concerns..
Air Berlin triggered bankruptcy proceedings in August after losing a cash lifeline from its biggest shareholder, Etihad Airways, and was grounded in October.
The European Commission said on Wednesday that Lufthansa's move was "regrettable" but that its offer for Air Berlin posed "clear risks to Austrian, German and Swiss consumers and to effective competition".
Lufthansa had already offered to give up many of the precious takeoff and landing slots it originally wanted under the deal, but Brussels saw this as "unsatisfactory," the airline said.
Niki's founder Niki Lauda, the Austrian former Formula One champion, said Thursday he was potentially interested in acquiring again the airline he sold to Air Berlin in 2011.
Lufthansa has been keeping Niki in the air with around 10 million euros per week, according to Bloomberg News.
Austria's Transport Minister Jörg Leichtfried said Thursday that up to 10,000 passengers could be stranded over the next two weeks but a spokesman later put the number at just over 5,000.
Efforts were underway to find space on existing flights operated by other airlines, and additional charter flights would then be organised if needed, the spokesman told the Austria Press Agency.
Wolfgang Katzian from trade union GPA told Oe1 public radio on Thursday that there were several other potential interested buyers for Niki, which employs some 1,000 people.