The site has been largely inaccessible for the last 24 hours, and the service is intermittent in the UK.
The Pirate Bay has confirmed the attack on its Facebook page, saying that it did not know who was behind it, although it "had its suspicions".
A provider of DDoS defence systems said that it was unlikely that the attack came from hacking group Anonymous.
"There will be further attacks, but what's significant about this whole story is that people think that it is the Anonymous attacking a site which is typically a type of site that they defend," said Andre Stewart of Corero Network Security.
"It could be the record labels, or a government somewhere that has had enough of not being able to catch The Pirate Bay, it could be just one person who had rented some cloud power from Amazon and is sitting in a cafe, and is able to launch an attack."
Although some users may have attempted to access the site using proxies, TPB itself warned them against doing so.
"Use proxies at own risk. Don't login unless you trust the proxy supplier. Don't freak out. You'll get your TPB fix tomorrow," said the site.
TPB allows users to illegally obtain copyrighted songs, films and other content for free.
Copyright holders argue this causes a significant loss in revenue.
However, others say that it is very difficult to assess the impact of downloading on sales.
"If they're losing money and seeing that the government is not being able to stop it, there's a real monetary value reason for them to try and bring it down," said Mr Stewart.
"And if they can do it in the name of Anonymous then it's great for them.
"Equally the governments that protect these industries are frustrated as well because they haven't been able to see it close down, unlike a number of other torrent sites."
Virgin Media began preventing access to the file-sharing site following a High Court order last week.
Some time later the Virgin Media website suffered a hack attack that many thought was organised to protest against efforts to block access to TPB.
Twitter feeds associated with the Anonymous collective wrote: "Virgin Media - Tango Down #OpTPB".
But TPB criticised Anonymous for the attack, writing on its Facebook page that it did not "encourage these actions".
"We believe in the open and free internets, where anyone can express their views," wrote TPB.
"Even if we strongly disagree with them and even if they hate us. So don't fight them using their ugly methods. DDoS and blocks are both forms of censorship."
File-sharing website The Pirate Bay (TPB) has been hit by a Distributed Denial of Service (DDoS) attack.