The crash happened on the A329 Oxford Road, at about 05:30 GMT.
Police said two of three people in the red Peugeot 206 involved were being treated in hospital.  A fourth is being sought by police.
The road has been closed while a structural engineer assessed the safety of two buildings, a hairdressers and a charity shop.
Thames Valley Police said inquiries were ongoing to establish the circumstances of the crash. No arrests have been made.
Motorists were advised to find alternative routes as lengthy delays were expected.  A diversion has been put in place.
A car ploughed into a row of shops in Reading, causing structural damage.