Craig Rivet was drafted by the Montreal Canadiens in the 1992 NHL Entry Draft from the Kingston Frontenacs in the Ontario Hockey League. He was drafted in the third round, 68th overall. Upon being drafted, he recorded junior career highs in 1992–93 with 19 goals, 55 assists and 74 points. He added 12 points in the playoffs as Kingston advanced to the semi-finals but were eliminated by the Peterborough Petes in five games.
After spending his first few professional seasons with Montreal's AHL affiliate, the Fredericton Canadiens, Craig Rivet earned a full-time roster spot with Montreal in 1997–98 and became an alternate captain to Saku Koivu during his time with the team. After a 25-point season with a career-high 8 goals in 2001–02, he re-signed with the Canadiens to a four-year, $12 million contract extension. In 2005–06, Rivet improved to 34 points, his best offensive output with the Canadiens.
With his contract set to expire at the end of the 2006–07 season, Craig Rivet was traded on February 25, 2007, to the San Jose Sharks with a fifth round draft pick in 2008 for Josh Gorges and a first round draft pick in 2007. This pick would later be used to draft current Canadien Max Pacioretty. Before becoming an unrestricted free agent in the off-season, he re-signed with the Sharks to a four-year, US$14 million contract, citing San Jose's fan base and competitiveness as major factors in staying with the club. He reportedly chose that offer over San Jose's offer of $12 million over the same timespan but with a no-trade clause. In the first season of his new contract, he recorded a career-high 30 assists and 35 points, topping all team defencemen in scoring (Brian Campbell finished with more points overall during the season, but only scored 19 of his points with San Jose).
On July 4, 2008, Craig Rivet was traded to the Buffalo Sabres with a 2010 seventh round draft pick in exchange for two second round selections in the 2009 and 2010 drafts. Before making his 2008–09 debut with the Sabres, he was named team captain on October 8, replacing Jason Pominville, the last to be named captain as part of the Sabres rotating captaincy the previous season. At the end of the 2009-10 season, it was revealed that Rivet's play in the previous two seasons had been hampered by a double labrum tear, for which he would have off-season surgery. Despite initial estimates of 4–6 months for recovery, which would have impinged on the start of the 2010-11 season, he was expected to return for training camp. Despite this, the veteran defenseman announced that the 2010-11 season might be his last in the NHL. Rivet was waived by Buffalo on February 23, 2011.
After clearing waivers on 24 February 2011, Rivet was reassigned to the Sabres' American Hockey League farm team, the Portland Pirates.
On February 26, 2011, Rivet was claimed on re-entry waivers by the Columbus Blue Jackets.
On October 10, 2011, Rivet signed a deal with the Elmira Jackals.
Craig Rivet has made one international appearance for Team Canada at the 2003 World Championships in Finland. He recorded 1 assist in 9 games as Team Canada captured the gold medal against Sweden 3-2 in the final.
Rivet currently co-hosts "The Instigators" with Andrew Peters on WGR 550 out of Buffalo.