The court's decision led to a wave of protests across Turkey and threatens to derail peace efforts between the ruling Justice and Development Party and Kurdish leaders.
CNN-Turk television reported that dozens of Kurdish youths had gone on the rampage in Bulanik, throwing stones and Molotov cocktails at banks and shops on the town's main street.
Television footage showed police firing tear gas to disperse the protesters, who hurled stones at a police armoured personnel carrier in the town, located about 350km west of Turkey's border with Iran.
DTP politicians announced on Monday that they planned to resign soon from parliament in a move that could lead to early elections in dozens of parliamentary districts.
The party also plans to appeal against the disbandment order at the European Court of Human Rights in Strasbourg, France.
Iraqi Kurds condemned the court's ban on the DTP on Tuesday.
"The president's office expresses its anger at the Turkish constitutional court's outlawing of the Democratic Society Party," said a statement released by the office of Massoud Barzani, the president of Iraq's autonomous Kurdish region.
"But at the same time it welcomes the policy of opening up adopted by the Justice and Development Party government," the document said.
"It hopes that the constitutional court verdict will not halt that process and calls on all Turkish factions to commit themselves to a policy of reconciliation so that it can be a success."
The 25-year-old conflict between the government in Ankara and Kurdish fighters seeking autonomy from Turkey has claimed tens of thousands of lives.