In the statement, a representative for Lea Michele said 'We ask that everyone kindly respect Lea's privacy during this devastating time'.
Lea is reported to be 'absolutely hysterical and completely inconsolable' at the death of her boyfriend of two years.
Cory, 31, spent Saturday with friends in his hotel room at the Pacific Rim hotel in Vancouver before heading out for the evening. He returned to the hotel alone later that night and was found dead by cleaning staff hours later.
No cause of death has been confirmed though the police have stated there are no implications of foul play.
Lea and Cory are understood to have dated for around two years, having played on screen couple Finn Hudson and Rachel Berry in the hit tv show, Glee.
Lea, 26, stood by Cory after he entered rehab for substance addiction in April and the pair were pictured just a month ago looking relaxed and happy.
Cory, 31, had battled substance and alcohol addiction throughout his life.
The star had spoken openly about the addiction issues that had affected him since his teens and told Parade magazine in 2011 that he began using drugs at 13, and by 19 went into rehab when his mother and friends intervened. He suffered a relapse earlier this year and checked himself into rehab again in April.
"He was a true joy to work with and we will all miss him tremendously."
Discussing her relationship with Cory in an interview in Marie Claire magazine in January of this year, Lea said: 'I don't even remember a time when he wasn't my boyfriend. No one knows me better than Cory. No one knows what it's been like to go through this more than he does.'
She continued, 'Feeling like you have that net underneath you allows you to jump higher and go farther. He makes me feel like I can do anything.'
'For the first time in my life, I feel really, really settled and happy,' she said. 'I feel like the luckiest girl in the world.'
A statement from Fox, the TV network behind Glee, issued a statement calling Monteith "an exceptional talent and an even more exceptional person".
"He was a true joy to work with and we will all miss him tremendously."
Tributes have flooded in from stars and fans across the world, with singer Taylor Swift, who dated Cory for a short period in 2010, posting on Twitter: "Speechless. And for the worst reason."
Rihanna tweeted: "Cory Monteith, may your spirit be at peace, and may you fly with the angels... Heartbreaking, my prayers are with all of his loved ones!"
While Kim Kardashian posted "Just heard about the death of Cory Monteith. So sad. Prayers 4 his family. Praying 4 Lea too! Words cant describe what they must be feeling,"