The play happened during the Texans preseason matchup with Miami on Saturday.
Smith will miss the Week 1 contest against the San Diego Chargers and was also banned the final two preseason games. His suspension will cost him $352,941 of his $6 million base salary this season.
"I didn't swing (the helmet) at him," Smith said, according to the Houston Chronicle. "I was restrained. I caught myself. I did it out of frustration, but I brought the helmet back slow to my body so I wouldn't hit him. I think the suspension is a little harsh because I restrained myself."
"I will appeal. Anybody would in this situation," Smith added. "I want to state my case. I've never had anything like this before. I'm surprised it included a regular-season game."