Born in Ceske-Budejovice, Czechoslovakia, Modry spent three years with his local club before joining Dukla Trencin in 1990-91. He was chosen 179th overall by the New Jersey Devils in the 1990 NHL Entry Draft and came to North America two years later. During his first season in North America, Modry adjusted well to the smaller ice surface and more physical style of play as a member of the AHL's Utica Devils.

After playing 41 games for New Jersey in 1993-94, the youngster no longer fit into Devils long-range plans. In July 1995, he was traded to the Ottawa Senators and scored 18 points in 64 games the next season. Before the end of the schedule he was moved to the Kings where he spent four years going back and forth between the minors and the NHL. During the 2000-01 season, Modry developed into a consistent NHL defenceman. He registered 19 points, plus/minus rating of +16 and looked steady when the club upset the Detroit Red Wings in the first round of the playoffs.

The 2001-02 season would be a career year offensively for Modry, finishing the regular season with 42 points before establishing a career high in goals with 13 in 2002-03. Modry's tenure with the Kings ended following the 2003-04 season, as the former Devils draft pick opted to sign as a free agent with the Atlanta Thrashers in the summer of 2004.

Modry would register 38 points in 79 games with the Thrashers before the club sent him to the Dallas Stars with teammate Patrik Stefan in exchange for Niko Kapanen and a 7th round selection in 2006. Modry would spend a half-season with the Stars before being sent back to his former club the Los Angeles Kings at the 2007 NHL trading deadline. In Los Angeles, Modrys veteran leadership helped a young core of Kings players during the 2007-08 season. However, with his contract set to expire in the summer, the Kings dealt Modry to the injury-plagued Philadelphia Flyers for a third-round draft pick in 2008.