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.
Torbay Council considers 'fire and re-hire' in pensions wrangle
'It would only be as a last resort and not a decision that we would take lightly'
110 extra officers for Devon and Cornwall Police
£4.7 million Home Office grant for region
Elderly pedestrian hit by car in Paignton crash
23-year-old woman arrested
Top up payments for Ukrainian hosts in North Devon
Households in the area to receive £425
Plans submitted to join two catholic churches in Barnstaple
Linked structures would 'enhance community value'
North Molton storm overflows halved
Water storage tank added at treatment works
