Tamil, a lion-tailed macaque, left his enclosure at Howletts on Wednesday.
Animal director Adrian Harland said the lion-tailed macaque group had several young males of a similar age and it was common for young male primates to fight as they became more dominant.
Keepers searching for Tamil have set humane traps in trees containing his favourite fruit and nut snacks.
They spent Wednesday looking for him in countryside surrounding the park near Canterbury and said searches would continue on Thursday.
Mr Harland said: "Thankfully the weather is relatively mild at the moment and we're hoping that when Tamil gets hungry enough, we can tempt him back with food."
He said Tamil would have received a shock from an electric fence when he escaped.
But he said the fences were designed to be a deterrent and not to harm the animals, and in this case the shock was not enough to stop him leaving.
A missing monkey is thought to have left his home at an animal park in Kent because of fighting within the group.