Smith was suspended for forcing off the helmet of Miami Dolphins offensive lineman Richie Incognito and swinging it at him during the team's preseason game last Saturday.
Part of Smith's punishment is that he also has to miss the Texans' last two preseason games. He will lose about $400,000 in salary.
Smith is allowed to practice through Aug. 30, but after that he is ineligible to participate in team activities until Sept. 10.
Houston opens the regular season Sept. 9 at the San Diego Chargers.
"In general, I feel disappointed, disappointed in myself that I was able to let him get to me in the way that he did that frustrated me, when knowing that that's his whole game, that's what he bases his skill level off of, and I let him take me down a road that led me into that path," Smith told KRIV-TV in Houston.
"Initially, I was full of frustration. I swung the helmet, but I didn't swing the helmet to hit Richie Incognito. If I was going to swing the helmet to hit Richie Incognito, it wouldn't have been hard. He's right there close. You can see how low the helmet was and how tight I brought it to my body."
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Former NFL wide receiver Terrell Owens is suing agent Drew Rosenhaus and his brother, Jason Rosenhaus, for $6.5 million.
According to Yahoo! Sports, Owens is seeking damages for breach of fiduciary duty, fraud, and negligence.
In the lawsuit, Owens claims that Rosenhaus introduced him to financial adviser Jeff Rubin and recommended that Owens hire Rubin to manage his finances.
He alleges that the now-banned financial adviser poorly invested his money, including in an illegal and now-bankrupt casino project in Alabama.
Owens claims that the advice given by the Rosenhaus brothers and hiring Rubin caused him to lose nearly $5 million, and another $1.5 million in income could have been generated if invested properly.
Rosenhaus declined to comment.
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The Pittsburgh Steelers acquired running back Felix Jones from the Philadelphia Eagles for linebacker Adrian Robinson.
Jones was a first-round pick by the Dallas Cowboys in 2008.
In five seasons with Dallas, Jones rushed for 2,728 yards with 11 touchdowns. He also caught 127 passes for 1,062 yards with three touchdowns.
Robinson signed with the Steelers as an undrafted rookie free agent out of Temple in 2012. He played on special teams in 12 games last season.
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New York Giants general manager Jerry Reese told ESPN radio that David Wilson will start at running back in the Sept. 8 opener against the Dallas Cowboys.
Wilson and Andre Brown are both listed on the team's depth chart as starters, but Reese said Wilson will be on the field first when the Giants open the season.
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The San Diego Chargers announced they agreed to a contract with cornerback Richard Marshall. Terms were not disclosed.
Marshall played in four games last year with the Miami Dolphins and had 17 tackles, one interception and one pass breakup before a back injury ended his season.
The Dolphins cut Marshall this week after attempts to trade him failed. He had five tackles and one pass breakup in three preseason games. He signed a three-year, $16 million deal with Miami last year.
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The NFL pressured ESPN into pulling out of a joint project with PBS' Frontline in producing a documentary about concussions, according to the New York Times. The documentary is set to air on Oct. 8.
Frontline and ESPN had been working on the investigation into head injuries for more than a year. While it will be televised in October, ESPN was pressured into backing out of the project after a film trailer was released earlier this month, the Times reported.
According to the report, NFL commissioner Roger Goodell, NFL Network president Steve Bornstein, ESPN president John Skipper and ESPN executive vice president for production John Wildhack met for lunch at Patroon, a Manhattan restaurant near the NFL's headquarters.
League officials reportedly expressed their opposition to the direction of the documentary, which implied that the league was looking the other way from evidence that players were sustaining long-term brain trauma.
"At no time did we formally or informally ask them to divorce themselves from the project," NFL spokesman Greg Aiello said. "We know the movie was happening and the book was happening, and we respond to them as best we can. We deny that we pressured them."