Tinordi, 21, appeared in six games with Montreal this season, recording no points and nine penalty minutes.
Last season, the six-foot-six, 227-pound defenceman split last season between the AHL and NHL, sharing top defenceman honours on the Bulldogs with Nathan Beaulieu.
In 67 regular season games with Hamilton, Tinordi recorded 13 points (two goals, 11 assists) and 71 penalty minutes. In eight regular season games with Montreal, he posted two assists and two penalty minutes. In five playoff games with the Habs, he had one assist and 15 penalty minutes.
On Tuesday, the Canadiens recalled Beaulieu and he played that night in the Canadiens' 4-3 loss to visiting Edmonton.
Hamilton’s next game is Friday when it hosts the Rochester Americans (Buffalo Sabres' affiliate) at Copps Coliseum at 7:30 p.m. ET.