The spokesman for the provincial governor said that about 600 protesters gathered in the southern town of Qalat on Wednesday, threw stones at police and set at least one police vehicle on fire.
He said: "Police were forced to fire into the crowd and wounded three demonstrators."
He later confirmed that two civilians who were wounded by the
shooting had died.
Seven Afghans have already been killed during protests in different parts of the country this week.
The cartoons were first published in a Danish newspaper in September but European newspapers reignited controversy last week when they reprinted them in a show of support for press freedom.
Protesters in Afghanistan have tried to attack the Danish embassy in Kabul and other foreign installations including the main US military base at Bagram, north of Kabul.
They have also turned their anger on police trying to stop them.