The 69-year-old Serb, who returned for a second stint as Levski coach in May, criticised the board for creating a negative atmosphere in the dressing room.
"I would like to leave because working under too much stress, in a bad atmosphere, I’m risking my health," Petrovic said in a statement.
He added that the club, aiming to replace him, had held talks with several coaches.
"I’m shocked," Levski owner Spas Roussev told local media. "A coach just can’t leave this way."
Petrovic watched Saturday's 2-0 win over Beroe from the stands while his assistant Asen Bukarev took charge.
Levski, searching for their first league title since 2009, are top with 27 points from 11 matches followed by champions Ludogorets who have 22 from nine games.
Petrovic became the eighth coach to quit or be sacked in the Bulgarian top-flight this season.
(Reporting by Angel Krasimirov; Editing by Tony Jimenez)
