"Lea started freaking out, she was distraught. No one knew what to say. It was horrible. She couldn't believe it," a source tells PEOPLE.
The call, the source adds, came from a friend who didn't want Michele, 26, to hear about Monteith's death at 31 from anyone else.
A friend of Michele's then suggested she leave home to avoid unwanted attention from paparazzi once news of Monteith's death became public.
"She needed to get out of her house, it was extremely emotional," says the source. "So she left and stayed in the home of her friend."
Since Monteith died on July 13 from a toxic mixture of heroin and alcohol, Michele has been grieving with his family and attended a private cremation ceremony last Tuesday in Vancouver.
"They are supporting each other as they endure this profound loss together," Michele's reps said in a statement, which also expressed Michele's gratitude for "all the love and support she's received from family, friends, and fans."
A different source told PEOPLE recently that the pair were discussing marriage and planned to walk down the aisle.
For much more on how Lea Michele is coping with the death of Cory Monteith, pick up the next issue of PEOPLE, on newsstands soon
Fans of Monteith may make donations in his name to three charities that were especially important to him: Project Limelight Society, which exposes youth living in Vancouver's Downtown Eastside to the arts; Virgin Unite, founded to support entrepreneurial efforts to better the world; and Chrysalis, which helps homeless and low-income individuals find employment.