Kearse, 26, signed with the Lions in March after four seasons in Minnesota, where he played in 62 games with five starts, making 79 tackles and defending eight passes.
Kearse was charged with DWI and carrying a firearm without a permit last October, when he was with the Vikings. Kearse apologized for his actions back in October, saying the arrest is "not a reflection of who I am as a person."
The NFL has not said whether this suspension is related to that October arrest.
"We were aware of the situation in free agency, obviously vetted the situation. We talked with Jayron and felt comfortable with him and the situation," Lions coach Matt Patricia said. "Obviously, [we] have gotten to know him a lot more since free agency and just felt comfortable with all of it. We knew it was something that was coming. ... It's a league matter, and I'll leave it at that.
"But it is something we were aware of during free agency."
Kearse is eligible to return Sept. 28 after the team's game at Arizona.
ESPN's Courtney Cronin contributed to this report.