As a youth, Hecht played in the 1990 and 1991 Quebec International Pee-Wee Hockey Tournaments with a team from Baden-Württemberg. The St. Louis Blues selected Hecht in the second round, 49th overall, of the 1995 NHL Entry Draft from Adler Mannheim of the Deutsche Eishockey Liga. Hecht played two full seasons for the Blues, compiling 32 goals and 46 assists before being dealt, along with Marty Reasoner and Jan Horáček, to the Edmonton Oilers for Doug Weight and Michel Riesen on 1 July 2001. After appearing in a full season with the Oilers, Hecht was traded to the Buffalo Sabres in exchange for the 31st and 36th picks in the 2002 NHL Entry Draft. As a Sabre, Hecht had his most successful NHL season, in terms of points scored, in 2006–07 with 56 points. Hecht was chosen as the captain for the month of October 2007 and later during February 2008. He is the second German-born player to captain an NHL team – Walt Tkaczuk was the first. The C was rotated monthly during the 2007–08 season. On 16 October 2007, Hecht agreed to a four-year, $14.1 million contract extension, which kept him in Buffalo until the 2011–12 season. Hecht scored his 300th career point on 26 October 2007, when he scored against Florida Panthers' goaltender Tomáš Vokoun. Hecht returned to the city of Mannheim with the Sabres to play against Adler in an exhibition game on 4 October 2011. Hecht, who was recovering from an injury and did not play, received a standing ovation upon skating onto the ice in pre-game practice. After being injured in January 2012 with a concussion, Hecht missed the remainder of the season and ended the year as a free agent. Several months into the 2012–13 NHL lockout, and after consulting with German doctors, he rejoined Adler, joining Sabres linemate Jason Pominville, who joined Adler as a lockout player. After the lockout ended, he re-signed with the Sabres to a one-year, $1 million deal. On 26 April 2013, Hecht announced his retirement from the NHL to reporters in the locker room following the Sabres' final regular season game against the New York Islanders. Following his retirement from the NHL, Hecht announced his intention to return to Mannheim to finish out his career. In 2015, he won his third German championship with the Adler squad. The first two titles came before his NHL career, in 1997 and 1998. Hecht played a total of three additional years in Germany before retiring from professional hockey in 2016.
Hecht was named player development coach for Adler Mannheim on August 2, 2016. He served as assistant to Marco Sturm, head coach of the German men's national team, during the 2016 Deutschland-Cup. In July 2017, Hecht was promoted to the assistant coach position at Adler Mannheim and parted company with the club in May 2018 to take care of getting his coaching licenses.