There was no immediate word on casualties in the explosion that took place in central Odessa in the early hours of Sunday.
The detonation was equivalent to one kilogram of TNT, according to the spokesperson, who said that the explosion damaged a Security Service building as well as the windows of a number of near-by residential houses.
Police have opened a criminal case in connection with the explosion, which is the latest in a series of blasts that have taken place in Odessa in the past few months.
All of these incidents have been described as acts of terror by law enforcement agencies.
On March 5, a powerful explosion ripped through an apartment building owned by the Ukrainian ultra-nationalist movement Right Sector; however, no one was hurt.
Odessa's worst terror act was the May 2, 2014 Trade Unions House Fire, in which dozens of anti-Kiev protesters were chased into the building before it was set alight.