Protesters are demanding that the local official in M’Sila province, an area some 200km southeast of the capital, Algiers, resign.
The protest came in the wake of the death of a local, Ayache Mahdjoubi, who fell into the 30-metre well on December 18 and was trapped there for six days.
They tried to storm the offices of the governor, chanting slogans in support of Mahdjoubi late into the night while calling for the governor to step down, before being pushed back by riot police.
Videos posted on social media on Tuesday showed hundreds of people involved in the protests, according to Aljazeera.
Some Algerians had faulted the pace of response by the authorities to the incident, pointing out that Mahdjoubi could have been rescued if civil defence units were deployed in time.
But officials in the rural district said rescuing Mahdjoubi required digging round a narrow 36-cm-wide pipeline, but the task was complicated by the overflow of groundwater around it.
Head of the Civil Protection Department, Colonel Ashour, told the Algerie Presse Service that “all efforts” were taken to save the 31-year-old.
Protests have been banned in Algeria under a decree issued in 2001 and the oil and gas-rich nation has a tightly controlled political system dominated by the military.