The 31-year-old veteran signed with New England on July 24.
This comes after Kendricks was sentenced to six months probation in July on a misdemeanor charge of marijuana possession. The charges were to be dropped if he completed eight hours of community service, with half that service set to take place at four Milwaukee high schools.
Kendricks spent the past two seasons with the Green Bay Packers. During 16 appearances and three starts last year, he hauled in 19 receptions for 170 yards and one touchdown.
He has 19 career touchdown catches in eight seasons.
Kendricks' suspension leaves the Patriots thin at tight end for the Sept. 8 season opener against the Pittsburgh Steelers. Five-time Pro Bowler Rob Gronkowski retired in March, leading the team to sign veteran Benjamin Watson in May. However, Watson has been suspended for four games following a failed drug test.
As a result, Matt LaCosse and Stephen Anderson are the top options on New England's depth chart.