Stoinis has been charged with a level 2 breach of the Cricket Australia (CA) Code of Conduct for personal abuse and was fined A$7500.
Stoinis later apologised for his behaviour and said: "I got caught in the moment and took it too far."
The incident comes two months after Victoria pacer James Pattinson was suspended for a Test match after using offensive language during a Marsh Sheffield Shield match against Queensland.
While Stoinis has been fined for his actions, Pattinson was handed two suspension points which ruled him out of the first Test of the summer in Brisbane.
Stoinis, however, starred for his side on Saturday as his unbeaten 55-ball 68-run knock along with skipper Glenn Maxwell's unbeaten 40 helped Stars hunt down a 143-run target with seven balls to spare.