Amalfitano was told to train away from Marseille's senior squad but the Frenchman ignored those repeated demands and reacted angrily towards Bielsa, who cut the session short as a result.
Some reports in France suggest Amalfitano, who was not selected for Marseille's 3-3 draw at Bastia in the opening round of Ligue 1 last week, spat at Bielsa.
Marseille released a statement confirming the 29-year-old would be punished by the club.
"Morgan Amalfitano joined the group to participate in the exercises, despite repeated requests from the technical staff inviting them to respect their decision," the statement read.
"Given the refusal of the player, Marcelo Bielsa decided to end the workout.
"Management of Olympique Marseille fully endorse the decision of the coach and the player will be summoned as soon as possible to inform him that the nature of the penalty that has been taken against him."
Amalfitano has been tipped to leave Marseille, with Premier League outfit West Ham a possible destination, after spending the 2013-14 season on loan at West Brom.
The former Lorient man scored four goals in 31 appearances at The Hawthorns.