Speaking on condition of anonymity, a spokesman from the governor's office said a colonel was among those wounded.
"One of the injured soldiers, a private, is in a critical condition and is being operated on," he said.
The blast shattered windows in the surrounding area, which was near a police housing complex in the Konak district.
Television footage showed dark smoke coming off a burning piece of wreckage in front of a police minibus as police cordoned off the area and warned civilians to stay away.
The explosion comes two days after a suspected suicide bomber pursued by police detonated a car in the southern city of Mersin, killing himself and wounding 12 officers.