Carkner was drafted by the Montreal Canadiens of the National Hockey League (NHL) with the 58th overall pick in the 1999 NHL Entry Draft; he never signed with the team, and ultimately signed with the San Jose Sharks as a free agent on June 6, 2001. In his first professional season (2001-02), the Sharks assigned Carkner to their minor league affiliate, the Cleveland Barons of the American Hockey League (AHL). In 74 games, Carkner had three assists, and 335 penalty minutes. He only appeared in 39 games the following seasons after suffering a knee injury in a game against the Utah Grizzlies on January 2, 2003, causing him to miss the remainder of the season. He came back with the Barons for the 2003-04 season as they qualified for the playoffs. In nine post-season games, Carkner had three assists and 39 penalty minutes. With the 2004-05 NHL lockout wiping out NHL play that season, he remained with the Barons the following season as well.