The 61-year-old Lloyd Webber's condition is in its early stages, a statement from his publicists said.
"Andrew is now undergoing treatment and expects to be fully back at work before the end of the year," the statement said.
Lloyd Webber recently announced plans for a sequel to his phenomenally successful musical "Phantom of the Opera." Called "Love Never Dies," it is scheduled to open in London in March and follow on Broadway in November. Rehearsals begin in the new year.
At a media event for the new musical earlier this month, Lloyd Webber said that while the story picks up where "Phantom" left off, he doesn't regard it as a sequel - "it's a standalone piece."
But Lloyd Webber said he was inspired to write the musical because "there's unfinished business."
In "Love Never Dies," the Phantom leaves Paris for Coney Island at the turn of the century, which Lloyd Webber said was like Las Vegas "and then triple it."
Producers say the original "Phantom" - a fixture of the London and New York stages - has been seen by more than 100 million people around the world. In September, it became the longest-running show in Broadway history, brushing aside Lloyd Webber's "Cats."
Lloyd Webber's other musical hits have included "Joseph and the Amazing Technicolor Dreamcoat," "Jesus Christ Superstar," and "Evita." He owns several theaters in London's famous West End.
According to his Web site, Lloyd Webber has won seven Tony Awards, three Grammy Awards, a Golden Globe and an Oscar. In 2006, he was awarded the Kennedy Center Honor.
Lloyd Webber was knighted in 1992 and named to Britain's House of Lords in 1997.