All were taken to the Royal Berkshire Hospital in the city for treatment, where they remain.
The police have now asked for information about the collision.
Sergeant Chris Howlett, the investigating officer, said: “I am calling on anyone who has witnessed this collision to contact Thames Valley Police on 101, quoting reference number 43230351708.
“I also urge anyone who may have dash cam, CCTV or camera footage of the collision or moments leading up to it to forcefully submit this via a dedicated portal for this investigation.
“Three people suffered minor injuries in this collision and the road has now been reopened.”