YouTube said the video - its most watched ever - has been viewed more than 2,147,483,647 times.
It has now changed the maximum view limit to 9,223,372,036,854,775,808, or more than nine quintillion.
Gangnam Style became a worldwide hit when it was released in 2012, largely due to the surreal video.
How do you say 9,223,372,036,854,775,808?
Nine quintillion, two hundred and twenty-three quadrillion, three hundred and seventy-two trillion, thirty-six billion, eight hundred and fifty-four million, seven hundred and seventy-five thousand, eight hundred and eight.
Why was Psy nearly too much for YouTube?
YouTube's counter previously used a 32-bit integer, which is a unit used to represent data in computer architecture. This means the maximum possible views it could count was 2,147,483,647.
On 1 December, it  posted a statement saying: "We never thought a video would be watched in numbers greater than a 32-bit integer... but that was before we met Psy."
Google, which owns YouTube, later told website The Verge that engineers "saw this coming a couple months ago and updated our systems to prepare for it".
YouTube now uses a 64-bit integer for its video counter, which means videos have a maximum viewer count of 9.22 quintillion.
Psy has yet to comment although news of YouTube's change was posted on his Facebook and Twitter pages.
The second most-watched video on YouTube - Baby by Justin Bieber - lags behind Gangnam Style by more than a billion views.

The Uefa general secretary has included the plan in his manifesto for the Fifa election on 26 February.
His idea follows European football's governing body Uefa's decision to play Euro 2020 in 13 different countries.
"Each confederation shall have to wait at least two editions before being able to host the World Cup again," he said.
"This will ensure a more equitable rotation, while giving every confederation the opportunity to organise this unique event.
"Furthermore, Fifa should investigate the possibility of organising the World Cup not only in one or two countries but in a whole region, so enabling several countries to enjoy the honour and benefits of hosting the World Cup."
Infantino is one of five candidates standing for the presidency of world football's governing body, which is in crisis following a series of corruption claims.
He is up against Sheikh Salman bin Ebrahim Al Khalifa, the Bahraini head of the Asian football confederation (AFC), Prince Ali Bin Al Hussein of Jordan, South Africa's Tokyo Sexwale and Jerome Champagne, a former Fifa deputy secretary general from France.
Current Fifa president Sepp Blatter has been banned for eight years from all football-related activities for breaching ethics rules.
The music video for South Korean singer Psy's Gangnam Style exceeded YouTube's view limit, prompting the site to upgrade its counter.
[NEXT_CONCEPT]
Fifa presidential candidate Gianni Infantino says he would press for the World Cup to be held in a whole region rather than one or two countries.