The 30-year-old Wright faces a misdemeanor charge of unlawful restraint, a misdemeanor charge of evading arrest and a misdemeanor charge of possession of marijuana. He remained in the Pearland City Jail on Thursday night pending a bond hearing Friday.
Pearland police said officers were investigating a disturbance in the police station parking lot around 11:30 a.m. Thursday. When officers approached Wright, he took off running and was eventually caught in a nearby subdivision.
"We had people on scene pretty fast and I believe because of our quick response time and the mental and physical toughness of our officers to catch offenders, we were able to get him in custody quickly and safely," Sgt. Roy Castillo said.
Police said they found 1.875 ounces of marijuana in Wright's vehicle.
A jail official told The Associated Press he did not know if Wright has an attorney. The Browns said they would not comment on the arrest Thursday night.
If found guilty on the unlawful restraint charge, Wright faces up to a year in jail and a $4,000 fine. If found guilty on the other charges, Wright faces up to six months in jail and a $2,000 fine on each charge.
Wright, who attended Northwestern State in Louisiana, was a fourth-round pick in the 1999 draft by the Minnesota Vikings. The nine-year veteran also has played for Houston, Jacksonville and Washington. He has seven career interceptions.
Houston television station KRIV first reported the arrest.
Pearland is about 15 miles south of Houston.