The prolific left-hander was found to have breached the International Cricket Council's code of conduct for players during the game on Saturday which the hosts won by 90 runs.
The incident took place during Sri Lanka's innings when Sangakkara got involved in a "prolonged discussion" with on-field umpire Bruce Oxenford in the 34th over, the ICC said in a statement.
Sangakkara was disputing the umpire's decision not to allow Sri Lanka to take the batting powerplay at that time, it said.
Sangakkara admitted the offence and accepted the sanction proposed by match referee David Boon after the game.
Boon took into account Sangakkara's "previous good record" and the fact that he apologised to the umpire at the change of innings.
Sri Lanka have clinched the seven-match series with an unassailable 4-2 lead. The last game will be played in Colombo on Tuesday.