The Nissan Micra crashed into the wall of the Citizens Advice office at the centre around 2.45pm on Tuesday.
The driver, a 77-year-old woman, was airlifted to Southampton General Hospital in a serious condition.
Structural engineers attended the scene to make the building safe, but the damage led to disruption for the Citizens Advice office, which had to close its doors.
A joint statement for Citizens Advice and the Forest Centre read: “An accident has taken place at the Forest Community Centre in Bordon that means our Bordon Citizens Advice office is structurally no longer safe for the public. The Forest Community Centre and Whitehill Town Council remain open. Our thoughts are primarily focused now on the wellbeing and quick recovery of the person injured in the accident.
“We have taken the decision to close the Citizens Advice in Bordon to the public this week and are putting in place plans to continue our service from next week.
“In the meantime, potential or current service users can come to our Petersfield or Alton offices (visit citizensadviceeasthampshire.org.uk for addresses) for advice or contact our advice line number 03444 111 306.
“We will keep the public fully informed as to when we will be able to return to the Citizens Advice offices in Bordon.”
Any witnesses should call Hampshire Police on 101, quoting incident number 482.