The animal rescue charity said it had been forced to close its shelter in Longridge Road until further notice.
It means the charity is unable to accept any animals from the public and adoption of its homeless dogs and cats has been put on hold.
There are currently four dogs and one cat listed for adoption and these will remain on site under the care of staff.
A spokesman for RSPCA Preston and District Branch said: "Following the UK Government announcement last night, we must close to the public until further notice.
"This means that we cannot accept animals from the public, and are looking after existing animals in our care, and new animals brought in via our animal rescue teams.
"If you have animal welfare concerns, please call our national cruelty line for advice: 0300 1234 999.
"If you have a badly injured stray or wild animal please call your local vet for advice. Please do not attend a vet practice without calling first.
"This is an incredibly difficult time for us across the RSPCA and we appreciate your ongoing support.
"As a self funded charity, who receives no government funding we rely heavily on public donations.
"As our charity shops have now closed, we need your help now more than ever to raise vital funds for the animal centre, any small donation can go a long way."
You can donate to the RSPCA Preston and District Branch here.