The Pfötli animal rescue service in Winkel in the canton of Zurich said it had taken charge of the cat, reckoned to be between two and three months old, on Monday.
Until now the male kitten had been cared for by a vet.
“He is a fighter and has got over his fever,” the shelter said on its website.
“He is a little shy at the moment, just sitting in his box, but he miaows when we speak to him.”
The shelter said a lot of people had expressed an interest in adopting the kitten but it would be several weeks before he could be released.
It said anyone interested in taking Oscar Fox should enquire in four weeks’ time.
The young cat arrived in Switzerland onboard a Swiss airlines flight from Athens last Wednesday.
He had survived freezing temperatures and a shortage of oxygen in the plane’s undercarriage to emerge the worse for wear from the aircraft in Kloten.
The Blick newspaper reported that the takeoff of flight LX 1843 from Athens had been delayed two hours as staff searched for the cat seen prowling around the plane before its departure.
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“A cat was prowling around the Airbus A321 in Athens. Suddenly it vanished,” said Swiss airline spokeswoman Myriam Ziesack.
“Ground staff thought it had got into the undercarriage, but after two hours of searching they still hadn’t found it,” said Ziesack.
Blick said airline staff had taken the cat to their hearts, christening it Oscar Fox after the last two letters of the airbus’s identifier – HB-IOF.