Hoo Zoo said it was likely that she was in the vicinity of the zoo, The Humbers, and surrounding fields where there was ample food and plenty of ponds.
They also said the escape had been reported to the council in line with the conditions of their licence.
“Under no circumstances should a member of the public try to capture the animal by themselves,” a spokesperson for Hoo Zoo said.
“Although capybara are generally friendly and inquisitive animals, the animal should not be approached as it could become unpredictable if alarmed or cornered.”
Anyone who spots Cinnamon between the hours of 17:00 and 09:00 BST is asked to call staff via an out of hours number, external and not report it via Facebook where comments might be missed.
A spokesperson for the zoo added: “Cinnamon has a fantastic bond with her keepers and it is likely that she can be encouraged back to her habitat with no physical intervention.
“Please wish us all the very best for the safe and swift return of Cinnamon. We appreciate all of your support in finding her.”