"It is important that Donovan use this time as best he can to resolve his personal situation," said Fox in a statement released to the media Sunday.
McNabb also took a leave of absence from NBC Sports Radio.
Jim Walsh of the Arizona Republic reported earlier in the month police in Gilbert, Arizona, arrested McNabb for alleged DUI, stemming from an incident on June 28:
A Gilbert police officer was called to a non-injury collision at about 11:35 p.m. on June 28 near Chandler Heights and Higley roads, where the officer found McNabb's silver Land Rover had rear-ended another vehicle.
According to a police report released Tuesday, McNabb struck a car driven by the wife of a Gila River Tribal Police officer.
"While Donovan spoke, I noticed a strong, fruity odor on his breath. I noticed Donovan's eyes were watery and very bloodshot and his speech was slurred,'' a Gilbert officer wrote in his report.
McNabb told police he'd been taking cough medicine, according to Walsh, and showed the arresting officers the cough drops in his mouth.
However, TMZ.com reported McNabb's blood alcohol level at the time of his arrest was .17, more than twice the legal limit in Arizona.
In April 2014, McNabb served one day of jail time after pleading guilty to DUI charges from an arrest in December 2013. As part of his guilty plea, nine days of his sentence were suspended.
After his most recent arrest, McNabb released a statement during his NBC Sports Radio show (via Pro Football Talk's Mike Florio).
"There was a story that was released, and I want everybody to be cognizant of it, because I am very aware of it, handling the matter at this particular point," he said. "But at this point, I have no further information, and as we continue on with the situation, then we’ll let it handle as it will handle itself."
Florio noted in a separate post Arizona law stipulates the 38-year-old could face at least 90 days in jail for a second DUI arrest, with the sentence potentially lasting as long as six months.
McNabb's broadcasting career began in 2012 after he joined NFL Network. In July 2013, Fox announced him as a panelist for Fox Sports Live, and his duties for Fox Sports broadened for the 2014 NFL season, when he worked as a color analyst with play-by-play man Dick Stockton.