Congo President's opponents accuse him of stalling the vote to cling to power, though his supporters deny the charge.
The radio station reported that police had tried to break up the evening demonstration by local members of the UDPS, the Central African country's main opposition party, led by newly returned exile Etienne Tshisekedi.
Elections were scheduled for November but the electoral commission said last month that Congo's voter registry will not even be complete until July 2017.
Kabila's opponents accuse him of stalling the vote to cling to power, though his supporters deny the charge.
However, donors and Western powers have pressured Kabila not to remain in power beyond when his mandate runs out on Dec. 19.
Lubumbashi lies in the heart of the copper belt of Africa's leading exporter of the yellow metal.
Kabila won disputed elections in 2006 and 2011 after succeeding his assassinated father, Laurent, in 2001. The constitution limits him to two elected terms, but the country's highest court has ruled he can remain in power until the election takes place, even if that falls beyond the end of his mandate in December.
If he does so, however, many analysts fear it could push Congo to the brink of another civil war, like the one that killed millions of people and sucked in half a dozen countries in the region between 1996-2003.
Dozens were killed in January 2015 in protests over a proposed revision of the electoral law.