Kendricks, 31, has been on the roster bubble as the Patriots have had an open competition among several players as they attempt to fill the void created by Rob Gronkowski's retirement.
The suspension is a result of a 2017 incident in Wisconsin, when Kendricks was cited for marijuana possession as part of a traffic stop. In July 2019, Kendricks was sentenced to six months' probation, and if he performed eight hours of community service, the charges would be dismissed.
The Patriots had signed Kendricks to a one-year deal on July 24. He spent the previous two seasons with the Green Bay Packers.
Kendricks is eligible to participate in all remaining preseason practices and the team's final preseason game Thursday against the New York Giants. He will be eligible to return to the Patriots' active roster on Sept. 9, after the team's Week 1 game versus Pittsburgh.
Kendricks played 24 snaps and had one catch for 11 yards in the Patriots' win over the Carolina Panthers on Thursday.
In a Week 2 preseason win over the Tennessee Titans, Kendricks also played 24 snaps and had one catch for 28 yards. He had been penalized for holding in the end zone in that game, resulting in a safety.
Veteran tight end Benjamin Watson, who also is vying for a roster spot, is suspended for the first four games of the season for violating the league's policy on performance-enhancing drugs.