The wicketkeeper and opening batsman was docked two demerit points and fined 30 percent of his match fee for his aggrieved reaction to being given out caught behind on Sunday, reaching five points and triggering an automatic ban.
Australia wicketkeeper Tim Paine was fined 15 percent of his match fee and received one demerit point for taunting Dickwella over the dismissal in Geelong.
Dickwella was punished after he paused to view the replay, kicked the turf and stared over his shoulder "for a prolonged period of time", an International Cricket Council statement said.
Sri Lanka clinched victory on the very last ball on Sunday when Chamara Kapugedera hammered a boundary, following Asela Gunaratne's 84 not out off 46 balls.