Faulkner has been fined 10 percent of his match fee after pleading guilty to violating an article of the International Cricket Council (ICC) code of conduct.
Faulkner bowled Gayle in the 38th over during Australia's series-clinching victory and responded by shouting in the direction of the batsman.
The ICC said Faulkner was fined for "using language or a gesture that is obscene, offensive or insulting during an International Match".
"The incident related to the bowler's actions after he dismissed West Indies batsman Chris Gayle in the 38th over," it said in a statement Thursday.
Faulkner, who finished with 4 for 48, pleaded guilty to the charge and accepted the sanction proposed by the match referee Ranjan Madugalle.
"There is no place for this type of behaviour anywhere near the game," said Madugalle.
"The players are expected to respect the opponents all the time. In this particular incident, James crossed the line and I'm sure he will learn from this incident."
However, there was support for Faulkner from his teammate Glenn Maxwell who tweeted that the Australian pacer was unfairly treated.
"@faulknerC25 copping unfair stick for today's (Wednesday) incident. Gayle wasn't even playing when he sprayed him in the PMs XI match."