The car hit a motorcycle, then crashed off the road, snapping a water pipe before crashing through the glass door of the shop, then ploughing onward through the store, stopping only when it reached the far end.
Police were told that 54-year-old Somsong Tirabatjek was overtaking a three wheeler on her motorbike on Yaowarat Rd when she was hit by the car, which was coming in the opposite direction.
The car driver then lost control and crashed into the Pumpui Apple clothing shop.
Ms Somsong had facial injuries and was taken to Vachira Phuket Hospital for treatment. The baby, suffering from head injuries, was taken to Bangkok Hospital Phuket.
The Toyota driver, who was not named, was taken for questioning by police.