The hour-long firefight followed a small explosion at around 8:30 a.m. local time (0130 UTC), which witnesses said came from a bomb made from a pressure cooker.
A man who authorities suspect blew up a cooking pot in Pandawa Park in Arjuna subdistrict in Bandung on Monday died en route to Sartika Asih Police Hospital after police shot him, West Java Police spokesperson Sr.
Police said it captured one suspect and reported no casualties.
Police had surrounded the building which was on fire and fired shots.
"We tried to negotiate but instead the perpetrator tried to burn (the place)", he told local TV station MetroTV.
"There's a possibility of JAD", said West Java police chief Anton Charliyan, when asked which network the attacker was from.
"He's from a terrorist network", he added, without revealing any further details.
Police say the situation is now under control, with one of the men being shot by police. After 2009 Indonesian Muslim militants have been targeting at symbols of the Indonesian state (rather than targeting at foreigners) due to the success of Indonesia's Police (especially Indonesia's anti-terror police unit called Densus 88) in the battle against terrorism.
A number of attacks and failed plots have been linked to IS supporters in Indonesia in recent years.