Saini starred in India's T20 win on Saturday by taking three wickets, but the International Cricket Council disciplined the bowler for the animated send-off he gave Nicholas Pooran, his maiden international wicket.
"Saini was found to have breached Article 2.5 of the ICC Code of Conduct for Players and Player Support Personnel, which relates to using actions or gestures which could provoke an aggressive reaction from a batter upon dismissal," the ICC said in a statement.
"He has also been handed one demerit point."
The player, who was described as a "rarity" by skipper Virat Kohli after his figures of 3-17, admitted the offence and accepted the sanction proposed by match referee Jeff Crowe.
When a player reaches four or more demerit points within a 24-month period they are converted into suspension points and a player is banned.
Two suspension points equate to a ban from one Test or two ODIs or two T20Is, whatever comes first for the player.
India won the second T20 on Sunday to take an unassailable 2-0 lead in the three-match series.