The NBA announced the suspensions Monday night following Cleveland's win to sweep Boston in the first round Sunday.
Smith swung backward and smacked Boston's Jae Crowder in the face. Smith was ejected and Crowder sustained a sprained knee ligament.
Smith will miss Games 1 and 2 of the Cavs' next series, when the club will also be without Kevin Love, who dislocated his shoulder earlier in the game.
Olynyk hurt Love, grabbing and pulling his arm. The league said Olynyk will serve his suspension in the first game of the 2015-16 regular season for which he is eligible and able to play.
Cleveland's Kendrick Perkins was also fined $15,000 and his flagrant 1 foul changed to flagrant 2 for a hard screen on Crowder.