Bianchi, who suffered a head injury while driving for the now defunct Marussia team, skidded off the track in wet conditions and collided with a recovery vehicle.
The Frenchman sustained a "diffuse axonal injury" which causes widespread tearing of nerve fibers across the whole of the brain, according to UK brain charity, Headway.
He returned to France last month and was treated at the intensive care unit of Le Centre Hospitalier Universitaire de Nice (CHU) before moving on to the rehabilitation center.
"As we reach the conclusion of a difficult year for our family, we wanted to take this opportunity to provide a further update regarding Jules' medical situation, per our pledge to communicate continued information, when appropriate, to his many fans," said the driver's parents, Philippe and Christine in a statement.
"It was a significant and very comforting step for us to be able to bring Jules home to France last month, to continue his rehabilitation surrounded by his family and friends. This is very important for Jules and also for us.
"Jules' neurological status remains unchanged; he is unconscious but able to breathe unaided. Whilst there is no significant information to report, we take a great deal of comfort from the fact that Jules continues to fight, as we knew he would, and this has enabled the medical professionals caring for him to commence the planned, but very painstaking, program of rehabilitation therapy."
Bianchi's parents say they will continue to provide updates of their son's progress and thanked the public for their ongoing support.
The statement added: "As we reflect on the events of the past few months, we would like to acknowledge once again the overwhelming warmth and affection shown towards our son. These continue to be challenging times for our family, but the knowledge that he has touched the lives of so many people all around the world has helped us through."
Earlier this month, the FIA published a report
which stated that Bianchi "did not slow sufficiently to avoid losing control" during his crash at the Suzuka circuit.
Bianchi's Marussia team folded in November after administrators failed to find fresh investment.
In the days after the crash, Marussia moved to address accusations that Bianch
i had not reduced his speed and that the team had actively encouraged him not to do so.
"The Marussia F1 Team is shocked and angered by these allegations," said the statement issued in October.
"At a time when its driver is critically ill in hospital, and the team has made clear that its highest priority is consideration for Jules and his family, it is distressed to have to respond to deeply upsetting rumors and inaccuracies in respect of the circumstances of Jules' accident.
"Regarding point 1, Jules did slow down under the double waved yellow flags. That is an irrefutable fact, as proven by the telemetry data, which the team has provided to the FIA.
"Regarding point 2, an audio copy of the full radio transmission between Jules and the team, and a written transcript, were provided to the FIA.
"It is quite clear from the transmission and the transcript that at no point during the period leading up to Jules' accident did the team urge Jules to drive faster or make any comments suggesting that he should do so."
The update on the French driver's condition comes a day after the first anniversary of Michael Schumacher's skiing accident.
The seven-time world champion is continuing his recovery from the severe head injuries sustained in a crash at the French ski resort of Meribel on 29th December last year.
Schumacher spent nine months in hospital in France following emergency brain surgery but was moved to the family home near Lake Geneva in Switzerland in September to continue his rehabilitation.
While the German's family declined to give an update on his condition, Formula One drivers and fans expressed their continuing support for the stricken driver on social media.