The Blues announced the trade on Wednesday, hours before the NHL trade deadline.
Labrie is 23 and had five goals, one assist and 69 penalty minutes for Manitoba of the American Hockey League. He was signed by Vancouver as a free agent in 2007. He will report to the Blues' AHL affiliate in Peoria, Ill.
Stastny has played in parts of four NHL seasons, all with the Blues, with six goals, 10 assists and 58 penalty minutes. He spent most of this season in Peoria. In four games with St. Louis, he had one goal.