Authority Chairwoman Gaynelle Hendricks said the meeting would focus on "security issues," WIAT-TV, Birmingham, Ala., reported.
The sign, which weighed between 300 and 400 pounds, struck Luke Bresette, his mother, Heather, and two brothers, Al.com reported. Bresette's mother and brothers remained hospitalized Saturday.
The Bresettes had been spending a spring vacation in Destin, Ala., and were at the airport to fly back to Overland Park, Kan.
A relative, Alex Bresette, said the boy's father, Ryan, and two other siblings were not hit. Heather Bresette had a broken pelvis and two broken ankles and was at UAB Hospital, where she underwent surgery Friday evening.
Sam Bresette, 8, had a broken leg, and his brother, Tyler, 5, suffered a concussion.
Witnesses said four men lifted the heavy sign and a total of eight held it up while rescue workers moved the victims.
Investigators were trying to determine Saturday what caused the sign -- which used digital readouts to display flight arrivals and departures -- to come crashing down.
Hendricks said airport authority President and Chief Executive Officer Al Denson and others were looking into the matter, and were holding "discussions with contractors, subcontractors that are responsible for the modernization of the ... airport."
The sign was located in a part of the airport open to the public before passengers reach security checkpoints, CNN reported. The section -- which features a children's play area, restaurants and a new baggage system -- had opened March 13, CNN affiliate WVTM, Birmingham, said.
Birmingham Mayor William Bell said after meeting with Ryan Bresette: "I cannot come close to understanding his heartache. But I will get answers."
Celebrity Families of 2014 [PHOTOS]