In the complaint, Universal singles out features on the website that enable users to save copies of videos to their profile pages or share them with others on the site.
In response to the lawsuit, MySpace issued a statement saying it was in full compliance with copyright laws and was confident it would prevail in court.
"Our music and videos play a key role in building the communities that have created hundreds of millions of dollars of value for the owners of MySpace," it said.
"Our goal is not to inhibit the creation of these communities, but to ensure that our rights and those of our artistes are recognised," read the statement.
Universal Music, a unit of Paris-based Vivendi SA, one of the world's major recording companies, is home to recording artistes such as U2, The Killers and Kanye West.