The 41-year-old, who has been a German Football Federation (DFB) referee since 1997 and had officiated in Bundesliga games since 2005, failed to show up for pre-game preparations with his assistants at their hotel two hours before Saturday's kick-off.
He was found by his assistants in his hotel room bath tub with his wrists cut.
His lawyer informed the DFB on Monday that his client's physical health was improving and he had left the hospital but had quickly sought treatment for his condition.
"It cannot be predicted how long this treatment will last," the DFB said in a statement.
Rafati's father told reporters on Monday he had repeatedly spoken to his son since the incident.
"He said he loved me. He wanted to apologise. I am very happy that he is OK," Djalal Rafati said.
DFB President Theo Zwanziger said on Saturday that the only explanation he could offer for the attempted suicide was that pressure on referees was "immense."
