Protesters besieged a police station in the central town of Niono, accusing the police commissioner of abuses.
"A horde of people armed with projectiles of all kinds ransacked the station and attacked the staff," the ministry's statement said.
Cop, security guard killed as 'drunken' men open fire in DHA
As police withdrew, Issiaka Tounkara was "caught and killed by protesters", it added.
A protester also died and a number of people on both sides were injured.
"Since his appointment, there have been more motorcycle thefts, robberies and looting," protester Issiaka Sanogo alleged.
The killing came as the United Nations (UN) mission in Mali, Minusma, said in a statement it was greatly concerned by a resurgence of violence since Wednesday evening in areas of Timbuktu in northern Mali.
Nine killed in Ohio shooting, assailant dead: police
Two girls travelling in a car were killed by gunfire in the town on Thursday, amid ongoing inter-communal tensions, a source close to the local government said.
Northern Mali fell into the hands of militants in 2012 before they were forced out by a French-led military intervention.
But much of the region remains chronically unstable and despite a 2015 peace deal with rebels, violence has spread to the multiethnic centre of the country.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ