The Canadian-born Monteith, who played star quarterback-turned-singer Finn Hudson on the Fox TV series about a high school glee club, was found dead in his room on the 21st floor of the Fairmont Pacific Rim Hotel on Vancouver's waterfront at about noon Saturday, according to police.
Acting Vancouver Police Chief Doug LePard said there was no indication of foul play.
Vancouver police said Sunday that an autopsy is expected to take place on Monday to determine the cause of death.
Monteith's body was found by hotel staff who entered his room after he missed his check-out time, LePard said. Monteith had checked into the hotel on July 6.
"We do not have a great deal of information as to cause of death," said British Columbia Chief Coroner Lisa Lapointe. She said further tests would be needed to determine how Monteith died.
"The exact nature of those examinations will depend on investigative findings within the next day or two as information is gathered from medical records and discussions with family take place," she said.
LePard said Monteith had been out with people earlier and that those people are being interviewed.
Video and electronic records from the hotel indicate Monteith returned to his room by himself early Saturday morning, and he was believed to be alone when he died, LePard said.
Lapointe said he had been dead for several hours by the time his body was found.
Lea Michele, Monteith's "Glee" co-star and real-life girlfriend, was asking for privacy after receiving news of his death, said her representative, Molly Kawachi of ID-PR .
"We ask that everyone kindly respect Lea's privacy during this devastating time," Kawachi said in in an email to The Associated Press.
Reality TV celebrity Kim Kardashian offered her condolences in a tweet: " So sad. Prayers 4 his family. Praying 4 Lea too! Words can't describe what they must be feeling."
"Glee" cast members and other celebrities also took to Twitter to express their feelings.
"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.
Lauren Potter, who plays Becky Jackson, the cheerleader with Down Syndrome on "Glee," tweeted that she feels "totally heartbroken right now."
"I love Cory so much this hurts my heart," she wrote. "I hope my Glee family is OK right now. I love them all. Cory was always so nice to me. I have so many good memories."
"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, called him an exceptional performer "and an even more exceptional person. He was a true joy to work with and we will all miss him tremendously."
"We are in shock and mourning this tragic loss," his representatives at Viewpoint Public Relations in Los Angeles said in a statement.
In April, Monteith checked himself in to a treatment facility for "substance addiction" and asked for privacy as he took steps toward recovery, a representative said at the time.
Michele told People magazine at the time that she loved and supported him and was proud he was seeking help.
It was not Monteith's first time in rehab. 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."
He told Parade magazine in 2011 that he was "lucky to be alive."
Monteith, who turned 31 on May 11, starred in "Glee" as 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 song-and-dance numbers and high-profile guest stars including Gwyneth Paltrow, became an immediate hit and made stars of its relatively unknown cast.
The series, which debuted in 2009, is in its fourth season.
On his Twitter account, Monteith described himself as "tall, awkward, canadian, actor, drummer, person."
In a 2010 interview with The Associated Press, Monteith was upbeat about life. He said that if "Glee" were to be canceled he would be OK.
"I've never been afraid of working," he said. "I've never been afraid of auditioning for jobs. Obviously, I've never been afraid of anonymity. I was happy (before 'Glee'). I'm happy now. I guess I'm well adjusted."
Monteith was among the "Glee" actors who remained series regulars as their characters graduated high school and moved on to other adventures.
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.
"Thanks for always being kind Cory. You came a long way from hanging on the beaches in Vancouver with the gang pre-Glee," tweeted Gerard Funk, an actor from Vancouver who joined the "Glee" cast last year.
Monteith's 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."
Monteith was an avid supporter of Project Limelight, a Vancouver charity that offers a theater and arts programs to at-risk youth. He dined with Project Limelight co-founder Maureen Webb at a Vancouver restaurant just days before his death.
In a Globe and Mail interview last year, Monteith credited Webb for suggesting that he enroll in acting classes when he was 19 years old and going down a "very dark path."
He kept in touch with Webb and made a video to support Project Limelight when the charity was launched last year.
"I think kids really need a place to go and feel like they belong," Monteith said in the video posted on Project Limelight's website. "When I was a kid, I struggled a lot with who I was and where my life was going and what I was interested in. And I was fortunate to have the arts inspire me."
Elber reported from Los Angeles. Associated Press writers Charles J. Gans and Frazier Moore in New York contributed to this report.