The 16-year-olds remain in hospital with the officers understood to have suffered minor injuries following the collision.
Police were called to the scene about 4.20am today with the ambulance service also attending the scene.
Officers remain on the scene.
It is understood the bike had been stolen at the time, but officers were not in pursuit.
Salters Road has now re-opened in the past hour between Musselburgh Road, Dalkeith, and Cowpit Road, Whitecraig, after being closed following the crash.
A Police Scotland spokesperson said: “Police in Midlothian are investigating following a road traffic collision on Salters Road in Dalkeith.
“The incident happened at around 4.20am on Wednesday June 13 when a motorcycle was involved in a collision with a police vehicle.
“Two 16-year-old youths were taken to the Edinburgh Royal Infirmary by the Scottish Ambulance Service.
“Inquiries are ongoing and anyone with information is asked to contact Police Scotland via 101, quoting incident number 0380 of 13 June.”
A number of drivers and the East Coast 140 service are being diverted as a result of the closure.
Drivers are being urged to plan ahead their route due to the closure and allow extra time if making a journey in the area.