Bianchi's parents, Philippe and Christine, arrived in Japan to see their son, who is at Mie General Medical Center following Sunday's crash into a trackside recovery crane.
Hospital officials declined to comment on Bianchi's condition Monday.
"Bianchi is in a serious but stable condition," FIA spokesman Matteo Bonciani told The Associated Press in a phone interview. "That's all I can say, and I'm doing this update on Jules' parents' behalf."
Bonciani added that Gerard Saillant, the president of FIA's medical commission who oversaw Michael Schumacher's treatment when the German was in a coma, also flew to Japan with Bianchi's agent, Nicolas Todt.
Bianchi crashed on the 44th lap in Sunday's rain-shortened race at the Suzuka circuit. His car went off at Turn 7, where Sauber driver Adrian Sutil had crashed two laps earlier. (Also read: Â Former F1 Driver Killed in Motorbike Accident)
According to a report issued by FIA, Bianchi lost control of his car, travelled across the run-off area and hit the back of the tractor that was being used to remove Sutil's car.
Bianchi was unconscious when he was taken from Suzuka to the hospital.
Sunday's race started at 3 p.m. local time. An approaching typhoon led to suggestions that the race would be pushed up to an earlier start, but it wasn't.
Four-time world champion Alain Prost, whose rivalry with the late Ayrton Senna is one of the greatest in the history of the sport, questioned the presence of the tractor on the track and said Bianchi's accident could have been avoided.
"A fundamental mistake has been made," Prost told TV channel Canal Plus. "It's been 20 years since we have seen a crash as serious as this one. This was not a race incident. It was obvious that the track was becoming dangerous. We need to find out where the mistake has been made and make sure it won't happen again."
Formula One has not suffered a death during a Grand Prix since Senna's fatal accident at Imola in the San Marino Grand Prix in 1994, where Roland Ratzenberger died the day before after a crash in qualifying.
"The new generation (of drivers) is not used to this kind of accidents," said Prost, acknowledging the security improvements made over the past 20 years. "This crash reminds me of the '80s, when we had this type of accident every two races."
At the time of Bianchi's crash, rain was falling steadily and it was getting dark. Several drivers complained of not being able to see properly.
Bianchi's family has already lost a member in a crash. In 1969, Bianchi's great-uncle, Lucien Bianchi, died in an accident during testing at the Le Mans race track when he crashed his Alfa Romeo into a post, a year after winning the prestigious endurance race.