Kennedy's suspension is effective immediately. He will miss games against the Bills, Dolphins, Patriots, and 49ers. Kennedy is eligible to return to the active roster Monday, Nov. 14.
Kennedy, 31, has four tackles in five appearances as a role player for the Giants. This is his first season in New York after spending the previous three in Minnesota.
Kennedy, who is from Yonkers, N.Y., was drafted 12th overall by the Rams in 2003.
The suspension was first reported by Howard Balzer of 101 ESPN Radio St. Louis.
Shortly after signing with the Giants in late August to provide depth on the defensive line, Kennedy said he felt the Giants were getting the best defensive tackle in the NFL.
"You ask me who the best defensive tackle is in the NFL, I'll tell you Jimmy Kennedy," Kennedy said. "Whether y'all believe it or whether I believe it in my head, that's all it takes."
Ohm Youngmisuk covers the Giants for ESPNNewYork.com.