Tigers general manager Al Avila announced on Friday that the team will not pick up the $16 million club option on Sanchez.
Instead the Tigers will pay him a $5 million buyout.
Sanchez, 34, had a difficult season. He was 3-7 with a 6.41 ERA in 28 appearances, including 17 starts. He allowed 26 home runs in 105 1/3 innings.
Sanchez accepted a demotion to Triple-A Toledo during the season with the hope that it would help him regain a spot in the Tigers' rotation.
He started nine games for the Tigers after August 1 and was 0-6 with a 4.88 ERA in those contests.
His best season was 2013, when he went 14-8 and was the American League ERA champion with a 2.57 mark. He finished fourth in the AL Cy Young Award voting that season.
The Tigers will look for a free agent to stick into its rotation.
"You may not see a free agent signing until maybe late January," Avila said, according to the Detroit Free Press. "We'll take the process a step at a time.
"Hopefully we can find a diamond in the rough somewhere or lightning in a bottle would be a better term. Trying to make sure we're put together a team that can compete solidly over the six months of the season."