The nine-minute clip, which shows Cruise touting himself and fellow Scientologists as "authorities on the mind", was a part of a video shown at a 2004 International Association of Scientologists meeting.
Scientology was founded by sci-fi writer L Ron Hubbard in the 1950s. It claims to be a religion, while many of its critics claim is it a cult. Celebrity adherents include 'My Name is Earl' star Jason Lee, John Travolta, musician Beck, Juliette Lewis and Kirsty Alley.
Cruise appears wearing a black turtleneck sweater and speaks animatedly about his dedication to changing people's lives and the world, while the musical theme from 'Mission: Impossible', the movie he starred in, plays in the background.
A statement on YouTube's site, which replaces the video, says: "This video is no longer available due to a copyright claim by Church of Scientology International."
A Google spokesperson said: "Google cannot comment on individual videos. Every original content creator on YouTube is a copyright holder, from amateur users to the largest media companies."
However, the video can still be viewed on many websites include Gawker.com, which has refused to remove the clip.
Nick Denton, Gawker.com publisher, wrote on the site: "It's newsworthy, and we will not be removing it."
During the video, Cruise erupts in bursts of laughter and hand-slapping as he talks about the "privilege" of calling himself a Scientologist.
"It's something you have to earn," he said.
"We're the authorities on getting people off drugs. We're the authorities on the mind. We're the authorities on improving conditions... We can rehabilitate criminals... We can bring peace and unite cultures."
He continued: "Being a Scientologist, when you drive past an accident it's not like anyone else. As you drive past, you know you have to do something about it because you know you're the only one who can help."
Last year, the BBC aired a Panorama documentary on the Church of Scientology, which was attacked by the group. A blog post on Brand Republic drew a large number of comments.
At one point during the documentary, BBC journalist John Sweeney lost his temper with Scientology representative Tommy Davis, which he later apologised for, but Sweeney and his editor defended the editorial integrity of the piece overall.
The organisation itself went so far as to create a website, bbcpanorama-exposed.org, to detail its objections to the BBC story and also produced a DVD, distributed free through the site, to tell its side of the story.