Little Jadan Brown still weighs less than three pounds, but his father, Larry, a trained emergency medical worker, told CBS' The Early Show that his son is doing very well.
"His health is great," Brown said, "They've been upgrading his status almost on a daily basis."
Jadan was delivered last Wednesday by his father and a Korean surgeon who happened to be onboard the flight from the Philippines to New York, the hospital said Monday.
"I really didn't have time to think about what was happening," Larry Brown, of Sicklerville, New Jersey, told the hospital.
Brown's wife Jacel was about seven months into her pregnancy when she started to go into labor in the middle of the 14-hour flight.
Jacel told Chen that she had been cleared to travel with the advice from her doctor that she should get up occasionally during the flight to walk around.
Once the couple realized that Jacel was going into labor, she asked her husband to carry her to the kitchen area, but because of a shoulder injury, he was unable to do that.
"At the time we didn't know that the baby was actually coming out - she had to walk from business class into the kitchen area and kneel down to allow us to remove her clothes. At that time, when I was able to remove her clothes, the baby was actually on his way out," Larry Brown told The Early Show.
The baby was born on the floor of the plane's galley at about 37,000 feet above northern Canada, the hospital said.
Jadan Brown was stabilized at a New York hospital after the plane landed, and was transported to Lourdes Medical Center late Thursday.
Dr. Sherrilynn Parrish, an obstetrician at Lourdes, said Monday that the baby and mother are doing well.
"This is really remarkable - especially since the baby was so premature," Parrish said.