In a post on Facebook this morning (Friday), the Kitty Cafe on Kirkgate say they had the windows smashed, donation boxes and tips taken, while the reception desk was destroyed in the process.
The cats are all thought to be fine as they were secured in the cattery.
The Kitty Cafe is closed while police investigations are ongoing.
The Facebook post says: "Thank you to the delightful ‘man’ who decided to smash our window to steal the cat’s donation boxes (he did leave 20p) and staff tips last night, and destroy the desk in the process.
"Luckily we have a fantastic security system and were alerted immediately - thanks ADT. The CATS ARE FINE and were secured in our cattery with our security lock system.
"They are being cared for by a member of staff and happily eating their breakfast."
Holly Cousins, Duty Manager of the Kitty Cafe, told the Yorkshire Evening Post: "It's been a targeted break in, they've taken money for the cats.
"There's a lot of mess and the window has been smashed.
"We're deeply upset but the cats are all fine, that's the main thing.
"Once we've cleaned up and got everything safe for the cats we will reopen."
Anyone wanting to make a donation to support the Kitty Cafe, you can visit this Justgiving page.
A West Yorkshire Police spokesperson said: "At 7am today (15/3) police received reports of a burglary at Kitty Café, in Kirkgate, Leeds.
"A window had been smashed in the early hours of this morning and donations boxes and till drawers stolen.
"The scene is due to undergo forensic examination and enquiries are ongoing."
Anyone who witnessed anything suspicious or who has any information that could assist the investigation is asked to contact officers via 101 quoting log number 253 of March 15 or crime reference 13190135558.