The Blue Cross charity centre had to throw out all 90 posts when they became saturated by drain water after torrential rain early on Friday.
All the animals were safe, although 15 kittens had to be evacuated from the nursery which was covered in sludge.
The centre has appealed for help to replace the posts and toys.
There are currently 46 cats and kittens looking for new homes at the charity's Garlic Row centre, animal welfare assistant Claire Thomas said.
The animals did not seem "too traumatised" by the torrential downpour or standing water in their pens, she said.
However, staff were "gutted" when they saw the devastation caused by the overnight storm.
The rescue centre was among a number of businesses and organisations in Cambridge affected by the overnight storm.
Addenbrooke's Hospital in Cambridge was forced to declare a "major incident" and cancel all planned surgery until Tuesday after an area where sterilisation equipment is stored was flooded.
The cat rescue centre has now been cleaned up and the destroyed posts, toys and blankets piled on the lawn.
It would not be sanitary to dry them out, Miss Thomas added, so they will all need to be replaced.
The Cambridge branch of charity Blue Cross cares for over 400 cats and kittens every year.

Danielle Marr, who is in her final year at The Waid Academy in Anstruther, Fife, has joined the RNLI crew in the town as a volunteer on local lifeboats.
In addition to her studies, Miss Marr will have to carry a pager and respond to emergency calls throughout the day.
She is following in the footsteps of her older brother Anthony.
She said: "I am delighted to join the crew here at Anstruther.
"I've grown up watching my brother volunteer and the difference the RNLI make in our community and I want to be a part in that.
"I've been on a few exercises on both the D-class and all-weather lifeboat and have really enjoyed the experience and look forward to continuing my learning."
The teenager is not the first pupil at The Waid Academy to be granted permission to leave class and rescue those in difficulties at sea.
Station coxswain Michael Bruce joined the RNLI more than 24 years ago when he was at school, and he said he is "delighted" to welcome Miss Marr to the station.
He added: "Having just completed her first exercise afloat since being enrolled, Danielle's enthusiasm to learn and become a competent member of the crew was clear to see.
"My team are looking forward to training with Danielle and preparing her for the challenges that will undoubtedly lie ahead.
"On behalf of the RNLI I would like to thank the Waid Academy for their supportive approach to pupils volunteering in the community and the benefits that come from doing so."

The Planning Inspectorate has backed the council's decision to demand the property near Crymych is demolished.
Owner's Charlie Hague and Megan Williams argued that the straw-walled house had low impact on the environment.
But inspectors said that did not change rules on building in rural areas.
"There is a lack of proper justification for the benefits of the low-impact development in this case for this matter to be given sufficient weight and to outweigh the policies which seek to control development in the countryside," ruled the planning inspector, Iwan Lloyd.
The owners had been living in a caravan for four years, before moving into the new home just before their son Eli was born.
Sculptor Mr Hague spent more than a year creating the single-storey dwelling from local materials.
The couple were helped by friends and relatives at the neighbouring Lammas eco village.
But Pembrokeshire council began enforcement proceedings earlier this year, after ruling it was an unauthorised dwelling built in open countryside.
Deputy council leader Rob Lewis said he welcomed the planning inspector's decision.
"Planning is a rigorous process with clear guidelines and if it is to be enforced fairly must also be upheld by everyone," he said.
The enforcement notice gives the couple two months to demolish the property.
However, the council will now consider a retrospective planning application for the house.
"It will be considered on its merits," said Mr Lewis.

Aarolina Rutkowska, 35 and of Cross Farm Road in the Peasley Cross area of St Helens, was found not guilty of murder after his trial at Liverpool Crown Court.
Mireslaw Kowalczuk, 29, was fatally stabbed in the chest at a house on Cross Farm Road on 27 December.
He died in the ambulance on his way to hospital.
Dozens of abandoned cats living at a Cambridge rescue centre have lost their toys and scratching posts after they were destroyed by flooding.
[NEXT_CONCEPT]
A 17-year-old schoolgirl has been granted permission to leave class to save lives at sea after becoming an RNLI volunteer.
[NEXT_CONCEPT]
A Pembrokeshire couple who built a 'hobbit-style' eco home without planning consent have lost a demolition appeal.
[NEXT_CONCEPT]
A woman has been cleared of murdering her partner who was found with stab injuries.