The six-foot-six Tinordi had two assists in 13 games with the Canadiens last season.
He had a goal and six assists in 44 games for the American Hockey League's Hamilton Bulldogs.
The son of former NHL defenceman Mark Tinordi was picked 22nd overall by Montreal in 2010.
He has played 43 career regular season games for the Canadiens, recording six assists. He has also appeared in five playoff games.