Undrafted out of the QMJHL, Viel signed a two-year entry-level contract with the San Jose Sharks in 2019. Playing the role of an agitating grinder, Viel spent two seasons in the AHL before getting NHL experience during the shortened 2020-21 season. He continued to split time between the NHL and AHL before spending the entire 2023-24 season in the AHL with the Manitoba Moose, the Winnipeg Jets’ AHL affiliate.