Two bombs exploded one after another at around 4:25 a.m. on March 18 in Tallinn's downtown area.
The explosions outside the AT sport shop, which sells sport and hunting goods, blew out the windows of four shops in the area and 30 apartment windows, but there were no injuries.
"The explosive could have been a substance with bolts and screws attached to it," said central criminal police spokesman Indrek Raudjalg.
A police bomb disposal unit later found two bottles containing another type of explosive material likely to start fires nearby.
Police closed off the site to pedestrians and drivers, but many attempted to get as close as possible for a glimpse of the destruction.
The explosions took place barely 100 meters from a popular hotel and Tallinn city administration headquarters.
"Everybody in my apartment woke up when the first explosion happened. We at once knew it was a bomb," said Vitaly, 30, who lives directly opposite where the explosions occurred.
Juri Merimaa, owner of the sport and hunting goods shop, told Aripaev Online he didn't think he had any enemies, had never received any threats, and that the shop was insured.
Trivimi Velliste, 54, an Estonian MP living on the street, told the SL Ohtuleht daily he saw two men running from the spot toward the French Lyceum located on a parallel street.
"I woke up after the first blast, looked out of the window and saw two young men wearing black masks running very fast toward the Lyceum sports ground," he said.
Rein Lang, Tallinn's deputy mayor, has a political version of the criminals' motive - a challenge for the Estonian state.
"Given that at least four foreign diplomats live on Roosikrantsi Street, we should look for the initiators of the explosion not among crooks settling scores but elsewhere," said Lang.
The police said they do not consider the version of Lang very serious. People whose windows were broken in the accident can apply to the municipal authorities for money to pay for repairs, the Tallinn central municipal district's press service said.