Police said 23-year-old Sam Miller and 24-year-old Tiffany Demitro were charged with reckless endangerment, acting in a manner injurious to a child.
Their one year old baby boy, Dillin Miller, was observed hanging from a the awning of a store on the first floor of their Third Avenue apartment building just after 10 a.m.
Dillin had apparently crawled through a piece of cardboard placed next to an air conditioning.
The child was left unsupervised by his parents, and was able to crawl onto a mattress next to the open window, and then crawl onto the fire escape.
The child fell off the fire escaped, tumbled down the awning and was about to fall to the ground but 44- year- old Christina Torre, who was biking past, was able to catch the victim before falling to the pavement.
She was on the phone with 911 trying to get the boy to hang on, when he dropped from the second story of this building.
"I just put out my arms when I saw him coming down, and luckily he landed straight in my arms on his back," Torre said.
The baby sustained lacerations to the face and was taken to Lutheran Medical Center in stable condition.
Three siblings - ages 2, 3 and 5 - were taken into custody by Administration for Children's Services.
The apartment was described as deplorable conditions. There was no food in the house, peeling paint, not adequate bedding for children, and no window guards.
"I am very proud of my daughter Cristina's actions today during an incident in Brooklyn involving a small child," said Joe Torre, now Major League Baseball's executive vice president of baseball operations, in a statement. "Fortunately for that child she was in the right place at the right time to lend a hand."
Joe Torre managed the Yankees from 1996 to 2007, where he won four World Series titles and six American League pennants. He had a 29-year career as a manager.
He retired after the 2010 season following three years with the Los Angeles Dodgers.
He played parts of 18 seasons in the majors, with nine All-Star appearances. He was the National League's MVP in 1971, when he led the league with a .363 average for the St. Louis Cardinals.