Cuan Wildlife Rescue's event was set to take place on Sunday in Stretton Road, Much Wenlock, but will not go ahead due to complications caused by the coronavirus pandemic.
In a statement online, the centre said: "We have been made aware of reports that our car rally is going ahead this weekend but unfortunately due to Covid-19 restrictions it won't be going ahead.
"We hope you can join us again in 2021 and we thank you for all your on going support in Cuan's busiest months."
This comes after the centre reported its busiest ever month in June this year, taking in more than 1,000 animals.
Throughout the month, the centre rescued 1,087 animals, compared to 753 during the same month last year and 779 in 2018.