The Frenchman suffered severe head injuries and underwent surgery after crashing into a recovery vehicle during the 2014 Formula 1 Japanese Grand Prix.
Marussia said updates about Bianchi's condition would be communicated in conjunction with the Mie General Hospital, and in accordance with the wishes of Bianchi's family.
"Following the accident involving Jules Bianchi during yesterday's 2014 Formula One Japanese Grand Prix at Suzuka Circuit, the Marussia F1 Team would like to acknowledge the huge outpouring of support and affection for Jules and the Team at this very difficult time," the team said in a statement.
"With regard to the communication of information concerning Jules' medical condition, we will respect, and be guided by, the wishes of the Bianchi family. Together with Jules' care, they will remain our highest priority.
"Therefore, we would ask for patience and understanding with regard to further medical updates, which will be communicated in conjunction with the Mie General Medical Center in Yokkaichi, where Jules is being treated, when they feel it is appropriate."
Representatives of the Marussia and Ferrari teams - Bianchi is a member of Ferrari's Driver Academy - will remain at the hospital to support him and his family.