Police said Griffin's hand was bleeding, and he "appeared intoxicated and unsteady on his feet." He was released after paying $1,750 bond.
"We've been in touch with Ryan," Texans general manager Brian Gaine told reporters after the draft. "We're aware of the situation. We commented on the matter, but as of right now, we're not going to comment on it anymore.”
Griffin caught 24 passes for 305 yards last season while playing in 14 games (11 starts). He has spent his entire six-year NFL career in Houston, largely serving as the team's second tight end before being their primary starter last season.
The Texans drafted San Diego State tight end Kahale Warring in the third round of April's draft. Houston will likely rely on Warring and Jordan Thomas to handle the tight end position next season.
Griffin seems likely to find a team to sign him, though he'll probably struggle to match the $2.3 million base salary he was due in Houston.