The accident happened about 1 p.m. as Brokaw was driving in the left lane of the northbound Bruckner Expressway in the Bronx.
Police and the Brokaws said a 1998 Ford Expedition swerved to avoid a spool of cable bouncing in the far right lane, which caused the driver of the SUV to lose control.
The Expedition overturned and then collided with the mail truck, police said. Suejas Estrada of the Bronx was thrown from the Expedition and killed. She was pronounced dead at the scene.
The Brokaws said the out-of-control Expedition forced the mail truck into the couple's lane. The truck collided with Brokaw's vehicle. Police said the mail truck's 54-year-old driver was taken to Westchester Medical Center with bumps and bruises. He was in stable condition Friday.
Brokaw, 69, and his wife, Meredith, said in a statement they were "greatly saddened by this loss of life." Brokaw didn't say in his statement where the couple was headed at the time.
The New York Police Department declined to confirm that Brokaw was involved in the accident. Police say they're investigating the accident.
Brokaw retired as NBC anchor in 2004 and was succeeded by Brian Williams. He has made frequent appearances on the network, filling in as anchor of the network's "Meet the Press" for months after Tim Russert's death in 2008.