Eric Weinrich was drafted 32nd overall in the 1985 NHL Entry Draft by the New Jersey Devils. In 1985-86, Weinrich enrolled at the University of Maine and scored 14 points as a Hockey East freshman. In 1986-87, he improved to 44 points in 41 games and was named an NCAA East Second Team All-American and in 1987-88 saw action in only eight games with the club before opting to join the U.S. National Team.
On January 29, 1989, Weinrich made his NHL debut against the Minnesota North Stars. After playing one more NHL game that season, Weinrich returned in 1989-90 and played 19 games while suiting up for the better part of the season with the Devils AHL affiliate in Utica where he was the recipient of the Eddie Shore Award as the league's top defenceman. That year, he scored his first goal and played his first six playoff games in the post-season. In 1990-91, he joined the Devils full-time and scored 38 points as a rookie.
On August 18, 1992, Weinrich was traded with the rights to Sean Burke to the Hartford Whalers for Bobby Holik and a second-round draft pick. In 1993-94, he was traded again, on November 2, to the Chicago Blackhawks as part of the three-team Steve Larmer deal that included the Rangers. In the shortened 1994-95 season, Weinrich scored 13 points in 48 games. In the playoffs, he helped his team reach the Western Conference finals before losing to the Detroit Red Wings in the Stanley Cup finals.
In 1998-99, he was traded on November 16 with Jeff Hackett, Alain Nasreddine, and a fourth-round draft pick to the Montreal Canadiens for Jocelyn Thibault, Dave Manson, and Brad Brown. In 80 games between the two teams, he recorded 22 points, 127 hits and 130 blocked shots.
In 2000-01, Weinrich served as Montreal's team captain early in the season when Saku Koivu was sidelined with injury. On February 21, he was traded to the Boston Bruins for Patrick Traverse, and on July 5, 2001, he signed as a free agent with the Philadelphia Flyers. Upon his arrival in Philadelphia, Weinrich was one of the team's more durable players and played his 1,000th game in 2002-03 before being dealt to the St. Louis Blues shortly after the 2004 NHL All-Star game. Weinrich went on finish the season with the Blues and following a lock-out year in 2004-05, returned to the club before having his rights acquired by the Vancouver Canucks at the 2006 NHL trading deadline.
After 1,157 career NHL games, Eric Weinrich officially announced his retirement from professional hockey on August 7th, 2006.
On the international stage, Weinrich represented his homeland on numerous occasions including; the World Junior Championships (1985-1986), the Winter Olympic Games (1988), the Canada Cup (1991), the World Cup (2004) and the World Championships (1991, 1993, 1997, 1998, 1999, 2000, 2001, 2002 and 2004).