Interfax, quoting local police, said the first explosion on Thursday, caused by a bomb, occurred outside the OMON base in Makhachkala in Dagestan, neighbouring Chechnya.
The agency said the blast occurred as a bus carrying OMON police officers arrived at the base. One of the injured was said to be a woman who was in a serious condition, but the others had only slight wounds.
An hour later, a second explosion took place about 50 metres from the base, Interfax said. No one was injured in this explosion, according to preliminary information.
Dagestan, on the Caspian Sea, has suffered from an overspill of violence from Chechnya where separatist groups are fighting Russian forces and has been the scene of kidnappings, killings and bomb explosions in the past five years.