The blue Honda Jazz smashed through a glass wall into the Yorkshire Cricket Museum in the east stand of the ground in Leeds, where members were holding a private party for club official Robin Smith.
One woman who was with the group is understood to have taken a glancing blow from the vehicle as it hurtled into the building just feet away from where she was standing.
She was taken to hospital after the incident this afternoon with what are believed to be minor injuries
The elderly driver, who is not thought to have been seriously hurt, was also taken to hospital where it is believed he was treated for shock.
Club spokesman Danny Reuben said Mr Smith was “a little bit shaken up, but fine”.
“They were very close,” he added.
“They were just about to go into the museum to have a look around when it happened.
“It is quite serious. The vehicle has gone through the wall through the museum and into the indoor cricket nets.
“The car is just lying embedded in the middle.
“It is difficult to know yet how much the damage will be.”
Leeds firefighters were called to the scene in St Michael’s Lane just before 4pm.
Police and ambulance crews also attended.
A spokesman for West Yorkshire Fire and Rescue service said the driver had not had to be cut free and crews had waited for the arrival of a structural engineer.
The scale of the damage is still being surveyed but it is hoped that events scheduled to be held at the stadium tonight will still take place.
Yorkshire County Cricket Club celebrates its 150th anniversary this year.