Police Scotland said their owner, a 36-year-old woman, was “extremely distressed”.
She had left the Keir Hardie Street property at 8pm yesterday and was out when the fire broke out at around 4.15am.
The force said: “The fire is being treated as wilful at this stage and enquiries are ongoing.
Detective Sergeant Clark Forrest, of Levenmouth CID, said: "Thankfully there were no injuries to anyone within the block of flats but the damage to the property and loss of the woman's kittens and cat has been extremely distressing for her.
"We're still trying to establish the full circumstances, so I'm appealing to anyone who has any relevant information or witnessed anything suspicious in the early hours of Saturday morning, or perhaps the days leading up to the incident, to contact us.”
"Anyone with information should contact us on 101 quoting incident number 0714 of 23 October.”