Police spokesman Gary Flot says McCray, 28, was stopped by an officer who saw him speeding about 4:30 a.m. Tuesday. He was booked into Orleans Parish Prison on charges of driving while intoxicated, speeding, careless operation of a motor vehicle and not having his vehicle registration with him.
A jail spokesman said McCray was released on his own recognizance around 7 a.m.
McCray refused to take a Breathalyzer test, police spokesman Janssen Valencia said.
"You have the right to refuse the test, but it has consequences," Valencia said. "Those include arrest and losing your license."
A person suspected of driving drunk in Louisiana and refusing the breath test automatically loses his license for one year.
Flot said McCray did not resist arrest.
McCray was signed to a five-year contract in March 2008, and took over as the starter during the last half of the season when defensive end Charles Grant was injured. He responded with 37 tackles (26 solo), the second-highest total of his career, and a club-high six sacks.
A seventh-round pick out of Florida in 2004, McCray played his first four seasons with Jacksonville.
This season, playing as a backup, McCray has appeared in all 15 games, and has 10 tackles and 1.5 sacks.
"We are aware of the situation involving Bobby McCray and we will let the legal process take its course," said Saints spokesman Greg Bensel.
McCray's attorney, Donald Foret, said he planned to talk to McCray and did not comment further.
The Saints (13-2) have clinched the NFC South title, a first-round bye. With Chicago's victory over the Vikings Monday night, they will play all their playoff games at home.
The players had Tuesday off.