Inspector Alexander Bastrykin said a man's apartment had been searched and bomb parts that "could have been used for the preparation of a homemade explosive device," had been found, the Novosti news agency reported.
The blast on a city bus during Wednesday's morning rush hour killed eight people and injured more than 50 others.
Bastrykin refused to identify the man or indicate if he been taken into custody but said the composition of the bomb was similar to one used by far-right group in a 2006 attack on a Moscow market that killed 11 people.
An unidentified regional police official said Tuesday's 4-pound bomb was designed for maximum carnage, the report said.
"The explosive device which detonated in the passenger bus had no solid encasement, and was packed with metal fragments, pellets, bolts and screws," the spokesman said.