Monteith was discovered by hotel staff in his room on the 21st floor of the Fairmont Pacific Rim Hotel on Vancouver's waterfront at about noon Saturday, according to police.
Staff went to check on him after he missed his checkout time, police said. Deputy Police Chief Doug Lepard said there was no indication of foul play.
"We do not have a great deal of information as to cause of death," Coroner Lisa Lapointe said. Lepard said Monteith had been out with people earlier and that those people are being interviewed.
Monteith was known to have struggled with addictions so fierce that he told Parade in 2011 that he was "lucky to be alive."
In April, he admitted himself to a treatment facility for "substance addiction" and asked for privacy as he took steps toward recovery, a representative said at the time.
Lea Michele, his "Glee" co-star and real-life girlfriend, told People magazine that she loved and supported Monteith and was proud he was seeking help.
It was not Monteith's first rehab stint. He received treatment when he was 19 and had previously talked about his addiction struggles, saying he had a serious problem and took just "anything and everything."
On the show, Monteith played Finn Hudson, a high school football player who puts his status and popularity at risk to join the glee club and its outcast members.
The show, with its pop music-based musical numbers and high-profile guest stars including Gwyneth Paltrow, became an immediate hit when it premiered in 2009 and made stars of its relatively unknown cast. The show is currently in its fourth season.
"I have no words! My heart is broken," Dot-Marie Jones, who plays football coach Shannon Beiste on "Glee," said in a post on her Twitter account Saturday night. She called Monteith a "hell of a friend" and an "amazing" man.
"What an absolutely tragic loss of a very talented young man," tweeted Zooey Deschanel, star of another Fox show, "New Girl."
Fox and the producers of "Glee," including 20th Century Fox Television, released a statement on Monteith's death.
"We are deeply saddened by this tragic news. Cory was an exceptional talent and an even more exceptional person," the statement read. "He was a true joy to work with and we will all miss him tremendously. Our thoughts and prayers are with his family and loved ones."
Monteith turned 31 on May 11. On his Twitter account, Monteith described himself as "tall, awkward, canadian, actor, drummer, person."
According to his biography on Fox's website, Monteith was born in Calgary, Alberta, and moved to Vancouver Island as a child. Before turning to acting, he held a variety of jobs including Wal-Mart greeter, school bus driver, roofer and cab driver.
Monteith's other TV credits included roles on the series "Kaya" and "Kyle XY" and guest appearances on "Smallville," ''Supernatural," ''Stargate," ''Flash Gordon" and "Interns." His film credits included "Final Destination 3," ''The Invisible," ''Deck the Halls" and "Whisper."
The Associated Press contributed to this report.