Ambulances, fire crews and police rushed to the scene of the incident on the A702 at Easter Howgate after receiving an emergency call at around 2.40pm this afternoon.
The collision involved a Nissan, Renault Clio and Ford Fiesta.
Fire crews said they were at work with hydraulic cutting gear to remove the roofs and other parts of two cars in which passengers were trapped.
Two women and a man were then taken to Edinburgh Royal Infirmary where they were treated for back and hip pain.
Two children, said to be under the age of 13, were also transported to the Sick Kids hospital and treated for similar complaints.
It is understood none of the injuries are life-threatening.
Police said the road was closed so a fuel spillage from the vehicles could be cleaned up and have appealed to the public for information.
A spokesman said: “Inquiries are ongoing into the full circumstances of the collision and anyone who has any information that can assist police is asked to call 101.”