It follows the outbreak of equine flu in horses.
A message on the charity's website says while their donkeys are not affected, they're closed as a precaution.
Four more horses have tested positive for equine flu - this time in Newmarket.
Racing is on hold until at least Wednesday while the British Horseracing Authority tests horses nationwide.
Two race meetings have been cancelled at Exeter Racecourse over the past week.
Pavement licence fees could rise in East Devon
A new policy has been adopted
Police appeal after phone theft scam
The money was never exchanged
Concerns for missing Devon man
Steven McCormick was last seen earlier this week
Exeter city centre toilets could become falafel outlet
They were closed in 2019
Torbay could quit blue flag scheme
It would save £260,000 a year
Voaden raises Slapton Line plight to PM
Sir Keir said communities had been “badly affected”
