Police have increased security at churches, mosques, shopping malls and airports as Indonesia, home to the world's largest Muslim population.
Following the attack, President Joko Widodo, who is from Solo and a former mayor of the town, urged calm and ordered police to quickly arrest others that may have been connected to the suicide bomber.
Police have increased security at churches, mosques, shopping malls and airports as Indonesia, home to the world's largest Muslim population, prepares to celebrate the end of the Islamic holy month of Ramadan.
"We are increasing the number of personnel, as well as intensifying patrols and security in places where there are a lot of people gathering," said police spokesman Agus Rianto.
Police said the attacker detonated the bomb he was wearing shortly after driving into the grounds of the police station in Solo, known as a hotbed for religious fundamentalism. A police officer who tried to stop him from entering sustained minor injuries.
The identity of the bomber was not immediately clear, but intelligence chief Sutiyoso told MetroTV he suspected the attacker was a supporter of Islamic State.
The radical group claimed its first attack in Indonesia last January, in the capital Jakarta, that killed four people. The four attackers also died.
Indonesia saw a spate of attacks in the 2000s, the deadliest of which was a nightclub bombing on the holiday island of Bali that killed 202 people, most of them tourists.
Police have been largely successful in destroying domestic militant cells since then, but they now worry that the influence of Islamic State could pitch the country back into violence.
Southeast Asian militants who claim to be fighting for Islamic State in the Middle East have said they have chosen one of the most wanted men in the Philippines to head a regional faction of the ultra-radical group that includes Indonesians and Malaysians, security officials said last month.