The league announced Lucic's punishment Sunday.
The incident happened five minutes into the second period of Calgary's 3-0 win. Lucic punched Sherwood behind the Flames net, knocking him to the ice, after Sherwood had poked at Calgary goaltender David Rittich's pads and received a slashing minor.
Lucic was assessed two minor penalties for roughing. Sherwood left the game but later returned.
The league said in an explanatory video that Lucic's history of "recent and similar punches" warranted the suspension. He has been fined once and suspended once for punching other opponents since 2016.
In his first season with Calgary, Lucic has three assists and 30 penalty minutes over 16 games.