The "Terminator 3" star has been missing since May 9 and Murphy, who reported him missing Monday, had said she was afraid he died from a drug overdose.
"I'm relieved," she told People magazine of Stahl's e-mail, which she called unemotional and unapologetic.
"But I'm also skeptical that he's really in rehab," she added.
Murphy said she did not receive a copy of the e-mail, but that it was sent to some of his friends Friday to let them know he would be out of touch for the next 30 days, TMZ.com reported Saturday.
Murphy said she was able to read the e-mail because she has access to his account.
A Los Angeles Police Department spokesperson told TMZ the missing person case would remain open because e-mail communication is not enough to close the file.
Notable deaths of 2014 [PHOTOS]