Hnat Domenichelli played midget hockey with the Edmonton Freeze. In 1992-93, he joined the WHL's Kamloops Blazers and scored 20 points as a rookie. In 1993-94, he scored 67 points and led the Blazers to a regular season championship. He then led the team to a WHL playoff championship and a Memorial Cup championship. In 1994-95, Hnat was a WHL West Second Team All-Star with 52 goals and 114 points and led the Blazers to their second straight Memorial Cup title. In 1995-96, he was a WHL West and CHL First Team All-Star with 59 goals and 148 points. He also won the WHL's Sportsmanlike Player-of-the-Year award and was also a member of Canada's gold-medal winning team at the World Junior Hockey Championships in 1996.
Domenichelli was selected 83rd overall in the 1994 NHL Entry Draft by the Hartford Whalers and in 1996-97 made his NHL debut with the Whalers. After splitting the early part of the season with Hartford and the AHL's Springfield Falcons, Domenichelli was traded to the Calgary Flames midway through the season.
The Edmonton, Alberta native spent parts of four seasons with the Flames organization before he was traded to the Atlanta Thrashers during the 1999-00 season. Coming off a career year offensively in 2000-01, Domenichelli was dealt to the Minnesota Wild where he has spent the past three seasons.