Staff killed Harambe in May after he grabbed a three-year-old boy who got into his enclosure.
Since then he has become a favourite subject of jokers, satirists and campaigners.
Responding, Cincinnati Zoo said the constant mentions were making it difficult for staff to move on.
"Our zoo family is still healing," director Thane Maynard told Associated Press in an email. "We are honouring Harambe by redoubling our gorilla conservation efforts and encouraging others to join us.''
Mr Maynard's twitter account was hacked over the weekend. The zoo's accounts have also been flooded with replies.
Harambe's death sparked huge controversy.
Debates touched on everything from whether zoo staff were correct to shoot him to why there was so much focus on him amid open conflicts elsewhere in the world.
The boy's mother has faced abuse online from those who blamed her for the death of the 17-year-old gorilla. Prosecutors ruled against pressing charges.
Cincinnati Zoo reopened its Gorilla World exhibit in June with a higher barrier in an attempt to prevent any more accidents.
After his death, numerous petitions have been created in Harambe's honour, some calling for him to be turned into a Pokemon Go character, to be put on a dollar, or carved into Mount Rushmore.
A poll in Texas suggested he would get 2% of the popular vote in the US presidential race.
Then there are the stream of jokes and references online.
But Harambe has been appropriated in nasty ways, such as in the racist abuse of actress Leslie Jones.
Retired Australian football player Adam Goodes also faced similar attacks online.
A zoo in Cincinnati, Ohio, says it is "not amused" by the numerous memes and petitions created after one of its gorillas was shot dead.