When users try and play the video it says the video is unavailable.
The original clips were posted by Vevo.
Several of the clips are still live at the time of writing although many of the titles have been changed to include names of the hackers.
Only some feature the replaced cover image, according to the BBC.
A Twitter account @ProsoxW3b - which allegedly belongs to one of the hackers - posted; 'It's just for fun'.
'Don't judge me I love YouTube,' the post said.
Despacito with its reggaeton beat went viral soon after its January 2017 release and found an even more colossal audience in April when pop star Justin Bieber appeared in a remix.
The Bieber version logged 12 weeks at number one on the US singles chart.
'Damn this really sucks. Despacito had 5 billion views on YouTube', wrote Dimeji Babalola, a computer scientist from George Mason University on his Twitter.
However, others users were more upbeat following the hack.
'Despacito got deleted off youtube, thank god', joked Uruguay-based Twitter user @Staraviamix69.
A Vevo spokesperson confirmed that a number of videos in its catalogue were subject to a security breach, which has now been contained.
'We are working to reinstate all videos affected and our catalogue to be restored to full working order', the spokesperson told MailOnline.
'We are continuing to investigate the source of the breach.' The videos in question were posted on YouTube.
'After seeing unusual upload activity on a handful of VEVO channels, we worked quickly with our partner to disable access while they investigate the issue', a YouTube spokesperson told MailOnline.
It was the first Spanish-language song to reach the top spot since 'Macarena' in 1996 and matching the 12-week reign earlier this year of Ed Sheeran's 'Shape of You.'
It beat the four-and-a-half-year run of Korean artist Psy's 'Gangnam Style' back in August last year.
In April last year hundreds of YouTube channels were hacked by OurMine, which claimed it was 'The biggest hack in YouTube history'.
Videos of compromised accounts showed posts that began #OurMine with the comment 'Hey, it's OurMine, don't worry we are just testing your security, please contact us for more information'.
The group is known for hacking high-profile social media accounts in order to shine a light on poor security, wrote the Sydney Morning Herald.
'We have no bad intentions and only care about the security and privacy of your accounts and network,' the group says on its website.
No long-term damage was done and the videos were turned back to normal within hours of the incident.
In May last year another groups of hackers posted step-by-step ransomware guides on YouTube instructing would-be attackers on how to create viruses.
The virus software that crippled the NHS could be bought for as little as £16 ($22) online and required little technical know-how to get up and running.
The video website deleted the videos uploaded by the hackers.
