The accident involving a 23-year-old woman and a 43-year-old man happened at 9.40pm on Thursday on the A702 at Hillend, close to the city bypass.
When fire crews arrived at the scene the female was out of her car and walking around but complaining of abdominal pain.
The other casualty had suffered a broken wrist and had suspected breaks in his legs.
Both were taken to the Royal Infirmary by ambulance.
A spokesperson for Lothian and Borders Fire and Rescue Service said: "Upon arrival the female was out of her car but fire crews administered oxygen to her and she had abdominal pains. The man had a broken wrist and suspected broken lower limbs."