The plane, which is operated by Loganair for Flybe, went off the tarmac and ended up on the grass verge, with its nose facing into the ground.
Two male passengers were taken to Western Isles Hospital, one suffering a back injury and one with an arm injury.
Another two female passengers also received minor injuries but declined medical assistance.
A police spokesman said: “The remaining 22 passengers and three crew were uninjured. A full air accident investigation has now been launched and will be carried out by the Air Accident Investigation Branch (AAIB) in conjunction with Police Scotland.”
Inspectors from the AAIB are now travelling to Stornoway to examine the scene.
The airport remains closed, although airport bosses have said they hope to reopen later.
Investigations start after four injured in Stornoway runway accident
