Griffin is facing charges of vandalism and public intoxication for allegedly punching out a front window in a hotel last month in Nashville, Tennessee.
The Texans took tight end Kahale Warring out of San Diego State in the third round of April's draft and also added free agent Darren Fells this offseason. Houston also drafted two tight ends last year -- Jordan Akins and Jordan Thomas -- so Griffin would have been competing for a spot on the roster even before his arrest.
Police in Nashville say hotel security followed Griffin after the window was broken, and when officers responded to the call, Griffin's left hand and fingers were bleeding and he appeared intoxicated and unsteady on his feet.
Police say Griffin, 29, was arrested for his own safety rather than given misdemeanor citations.
A friend of Griffin's said he had been overserved, according to multiple reports.
Griffin had 24 receptions for 305 yards last season with Houston and has 136 career receptions and seven touchdowns in six seasons.
A court date in the Griffin case has been set for May 31.
ESPN's Sarah Barshop and The Associated Press contributed to this report.