"The murder was committed on the night of January 6-7 in the Alapayevsky district. The body of the priest of the local Peter and Paul Church was found at the site after a fire," the department said.
In line with the old Julian calendar, the Russian Orthodox Church celebrates Christmas Day on January 7.
Probably, the robbers set the church on fire to conceal their crime, the department said.
More than 20 icons have been stolen from the church, the department said.
Local police, prosecutors and investigators have managed to solve the crime quickly. They have detained two suspects who are local unemployed residents with crime record, the department said.
"Proofs of the suspects' involvement in the crime have been gathered. A part of stolen icons has been seized from them and the remaining icons have been found at the local cemetery where the robbers hid them," the department said.
A criminal investigation into the murder has been launched, the regional interior department said.
The Moscow Patriarchy is shocked by the priest's murder, head of its press office said.
"Lately, we have been hearing ever more frequently about tragic events linked with the life of priests. This becomes a dangerous profession," Vladimir Vigilyansky said.
These developments speak about an appalling moral state of society, in which we live, Vigilyansky said.
"The murder of any human is always a tragedy and horror. The murder of a priest during Christmas holidays is shocking. It makes every person's heart weep," Vigilyansky said.