General Manager John Mozeliak said the decision to let Kennedy go was in the best interest of both the player and the team.
The 33-year-old Kennedy was facing competition from a half-dozen players for the second-baseman's job and requested a trade.
The Cardinals, unable to make a trade for Kennedy, had placed him on waivers before announcing his release.
"As stated last year, it has been our intention -- at Adam's request -- to try and seek a trade," Mozeliak said. "As we move forward, we feel that it is best to try and fill the second base position with other players from within our organization."
Candidates for the position include Brendan Ryan, Tyler Greene, Brian Barden, Skip Schumaker, Jarrett Hoffpauir and Joe Thurston.
Kennedy batted .280 with two home runs, 36 RBI and 42 runs scored in 115 games with the Cards last season. His career stats with the Cardinals and Los Angeles Angels include a .276 average, 57 homers and 423 RBI.