Burgess was whisked away by his partner outside the club's training centre prior to their morning session.
The England international was forced to walk out of the front doors of their Heffron Park base and front a media scrum.
Burgess indicated he would make a statement in due course but said: "I wish the boys all the well (sic)."
Club chairman Nick Pappas left soon after Burgess and said: "We wish Sam all the best."
Burgess - a club legend who holds a close bond with club co-owner Russell Crowe - has clashed with head coach Jason Demetriou.
Burgess is set to join Super League club Warrington next year.
Both Burgess and fellow assistant coach John Morris are believed to have raised concerns over Demetriou's preferential treatment of superstar fullback Latrell Mitchell.
Morris' future was unclear after Burgess' hasty departure on Wednesday but the loss of two assistant coaches will only ramp up the pressure on Demetriou as he battles to steer Souths into the finals.
If Morris, who has been linked to becoming Benji Marshall's No.2 at Wests Tigers next season, also walks away from the club, Demetriou will have just one assistant coach, Ben Hornby, ahead of the Rabbitohs' final game of the regular season.
A late season implosion has left them needing to beat bitter rivals the Sydney Roosters next week to guarantee they make the top eight.
Souths haven't missed the finals since 2017 and their case hasn't been helped by the fact Mitchell was suspended on Tuesday for dangerous contact in Sunday's lacklustre loss to Newcastle.
Mitchell's application has been the elephant in the room at the Rabbitohs all season.
Some at the club have raised concerns over his fitness and dedication after missing 10 weeks of the season with a calf injury.
The Australia international was spotted downing beers on stage with country singer Luke Coombs last week, only to turn in an anaemic performance against Newcastle with Souths' season in the balance.
12°C