The move comes a day after the Cincinnati Zoo said it was "not amused" by enduring memes over the gorilla's death.
Staff members fatally shot Harambe in May after a three-year-old boy climbed into his enclosure.
The death was subject to controversy, prompting angry tweets and petitions.
Zoo 'not amused' by Harambe memes
Cincinnati Zoo director Thane Maynard said on Monday the staff was "still healing" from the incident and the outpour of online memes and satire was making it difficult to move on from Harambe's loss.
The 17-year-old gorilla's death sparked international outrage and the boy's mother faced online scrutiny regarding her parenting skills.
Prosecutors decided not to press charges against the mother.
The zoo reopened its Gorilla World exhibit in June. The exhibit included reinforced barrier designed to prevent further accidents.
But online, numerous memes, petitions and hashtags such as #JusticeForHarambe cropped up in the gorilla's honour. Over time, Harembe became popular shorthand in social media humour.
Some pranksters called for the animal to be put on the dollar bill, while a poll in Texas suggested he would receive 2% of the popular vote in the US presidential election.
The memes took a racist turn in June when retired Australian football player Adam Goodes and Ghostbusters actress Leslie Jones were compared to an image of Harambe.
Mr Maynard's Twitter account was also hacked over the weekend.
The zoo's Twitter account was continuously flooded with references to Harambe before it was erased on Tuesday. For every Tweet they posted, no matter the subject, the zoo received dozens of replies referencing the gorilla.
An Ohio zoo where a gorilla was shot and killed has deleted its Twitter account after constant online harassment about the animal's death.