The hard-nosed winger received a match penalty at 15:54 of the third period in Boston's 4-1 win Thursday over the Thrashers.
Meyer levelled Lucic with a high hit sparking a wild line brawl. Once the players packed together in between fights, Lucic dropped Meyer with a clean shot while both players were being restrained by officials.
The disciplinary hearing took place Sunday with Lucic "fined $2,500 for the punch thrown in the scrum and $1,000 for making an obscene gesture directed at the Thrashers bench," Bruins general manager Peter Chiarelli said in a statement.
"The NHL has informed us that Milan will not be suspended," Chiarelli added. "He will join the team on the flight to Florida and be available for Monday's game against the Panthers."