Protesters have set up barricades and torched cars on one of the main roads in the Democratic Republic of Congo’s capital, a BBC correspondent says.
The opposition says Mr Kabila is trying to delay the poll in order to remain in power beyond his two-term limit.
The electoral commission was meant to announce a date for presidential elections, due in November, on Monday.
Protesters had planned to march to the commission’s headquarters to demand a precise election timetable.
Police have made at least 10 arrests, with hundreds of protesters out on the streets, reports BBC Afrique’s Poly Muzalia from the capital.
Most schools and shops are closed in Kinshasa, with those not involved in the protests staying inside to avoid any trouble, our reporter adds.
Election officials and the government say the poll may have to be delayed because of difficulties in organising them in the vast central African state.
A government-backed effort to work out a solution to the political crisis, called a “national dialogue”, has been boycotted by most opposition parties.
Mr Kabila’s second term, the maximum allowed under the country’s constitution, is due to expire on 20 December.
DR Congo has never had a smooth transfer of power since independence more than 55 years ago.