Griffin will not be allowed to practice this week and will miss the Titans' game against the Indianapolis Colts. His appeal was denied Tuesday, a source told ESPN's Josina Anderson.
Rivera was knocked out of the game after the hit and was diagnosed with a concussion.
"All I can say is I apologize to the Titans fans, my teammates and the organization," Griffin said in a text message to the (Nashville) Tennessean. "I also hope Rivera is doing well and I apologize to [Rivera] and his family. I was trying to do my job but in the end I hurt the team."
He also apologized through his Twitter account and indicated that he planned to appeal the suspension. He had three business days to make that decision.
Up costing my team. Don't know what else to do except for appeal. Again I apologize.
— Michael Griffin (@MikeGriff33) November 25, 2013
Rivera was trying to catch a deep pass from Raiders quarterback Matt McGloin when Griffin came in and lowered his helmet on the hit. Rivera's helmet flew off after the contact, and he did not hold on to the ball.
Griffin was penalized on the play, and Rivera stayed down for a few minutes before walking off the field under his own power.
The NFL said Griffin's illegal hit on Rivera was his second such violation this season and fourth since 2011. All of Griffin's violations have been for striking defenseless players in the head and neck area, the league said.
Titans teammate Bernard Pollard, who has been fined multiple times himself by the league for hits, took to Twitter on Monday to blast the NFL's safety rules after Griffin's suspension was announced.
We wear pads for a reason! Take the Defense off the field! You fine us for playing ball! 1 man and his minions. Show me where the $ going!
— Bernard Pollard Jr (@Crushboy31) November 25, 2013
Information from The Associated Press was used in this report.