The 37-year-old now will go on waivers.
The decision to part ways was mutual, Kingsbury said. The Cardinals have been discussing Suggs' future with the team throughout the season as his role continued to decrease, according to the coach. The Cardinals also want to start using more younger players.
However, Kingsbury said that neither Suggs' injury history this season nor the team's decision to move Haason Reddick to outside linebacker factored into the decision.
Suggs has sat out 10 of the Cardinals' past 14 practices due to hamstring and back injuries and an illness, according to the team's injury report.
"It was mutual conversations as the thing went on," Kingsbury said. "The respect was both ways, and we know what he's meant to this league, the Hall of Fame player he's been, and so we just wanted to have those conversations."
The seven-time Pro Bowler is one of the most accomplished pass-rushers in NFL history, ranking first among active players with 138 sacks. He played 69% of Arizona's defensive snaps this season and started all 13 games, collecting 5.5 sacks.
It's uncertain if Suggs will want to continue playing, but he will be on waivers until Monday, after which he'll be free to sign with any team if he goes unclaimed.
"We have such great respect for him," Kingsbury said. "He was phenomenal in our building, work ethic, energy, the juice he brought every day, professionalism -- it was through the roof, and so we wanted to give him an opportunity to find a fit if that's out there."
Suggs, the longtime face of the Baltimore Ravens' defense, signed a one-year, $7 million deal with the Cardinals in March that was fully guaranteed. He is the latest veteran the Cardinals have released, following wide receiver Michael Crabtree on Sept. 23, safety D.J. Swearinger on Sept. 30 and cornerback Tramaine Brock on Dec. 2.
Known for his leadership, durability and passion, Suggs was the NFL Defensive Player of the Year in 2011.