Two groups of hounds were chasing a fox and deer when they got into the Greenacres Animal Sanctuary site near Hastings on Tuesday.
The dogs from the East Sussex and Romney Marsh hunt had to be rounded up by hunt members and Sussex Police.
The Celia Hammond Animal Trust, which owns the sanctuary, said 60 cats escaped, with 10 of them still missing.
“The huntsmen apologised to the owners right away for any inconvenience caused,” a hunt spokeswoman said.
Trust founder Celia Hammond, said: “I had a hysterical phone call from the management saying there were hounds in full cry.
“The horns were going and they were trying to get the hounds back but nothing was happening. They were here for about an hour and a half.
Bolted and chased
“Whether [the cats] have been driven off our sanctuary and have bolted and been chased or whether they had been run down, grabbed and killed, we just don’t know,” Ms Hammond said.
The East Sussex and Romney Marsh Hunt, said “a few” of its hounds may have been distracted by the fox and deer from their pre-laid scent trail.
A spokeswoman said: “Although nobody from the hunt witnessed hounds following anything other than their original trail, it is suspected that a few hounds might have deviated from their trail on to the scent of a live quarry which they followed into the wildlife sanctuary.
“The hunt staff immediately removed the hounds.”
A police spokesman said: “The circumstances are being reviewed by a dog legislation officer to establish whether any criminal offences have taken place. If so, they will be investigated.”
BBC contributed to this report.