Monteith, who plays Finn on the popular Fox television series, "asks for your respect and privacy as he takes the necessary steps towards recovery," the publicist's statement said.
The statement said Monteith's decision to seek treatment at the facility was voluntary. It offered no details on the nature of the addiction other than that it was a "substance addiction."
The Canadian actor has starred on the musical series since 2009 as singing jock Finn Hudson, but was expected to be absent from the show's final episodes later this season.
Lea Michele, Monteith's girlfriend and "Glee" co-star, issued a statement saying, "I love and support Cory and will stand by him through this. I am grateful and proud he made this decision."
In recent years Monteith has openly discussed having had what he characterized as a serious drug problem during his early teenage years, and entered a treatment facility at age 19.
(Reporting by Chris Michaud; Editing by Eric Kelsey and Jackie Frank)