"I love and support Cory and will stand by him through this," Michele, 26, who's also his girlfriend, said in a statement. "I am grateful and proud he made this decision."
Murphy tweeted Monday, "I am so proud of Cory Monteith and love and support him 100%." Additionally, the show's producer, 20th Century Fox Television, said in a statement, "Cory is a beloved member of the 'Glee' family and we fully support his decision to seek treatment. Everyone at the show wishes him well and looks forward to his return."
A representative for Monteith, 30, told People magazine Sunday night that the actor "has voluntarily admitted himself to a treatment facility for substance addiction. He graciously asks for your respect and privacy as he takes the necessary steps towards recovery."
Fox told Deadline.com that filming of the musical dramedy's final two fourth-season episodes will proceed as scheduled, with an explanation given for the absence of Monteith's character, Finn Hudson.
Monteith had previously been in rehab when he was 19. In 2011, he reflected to Parade magazine that he was "lucky to be alive" after years of teen drug abuse. By 13, he said, he was skipping school to smoke pot and get drunk. "I had a serious problem," Monteith remembered, abusing "anything and everything, as much as possible."