AVA- The attack targeted Al-Zahra mosque in Qalae Amir Mohammad Khan area in the Police District 2 of the provincial capital, also Ghazni.
Nasir Ahmad Faqiri, provincial council member, said a man who was guarding the mosque was injured in firing from a nearby garden.
There was no immediate claim of responsibility for the attack.
Ashura commemorates the martyrdom of Imam Hussein (AS), grandson of the prophet Mohammad (PBUH).
This year, Ashura is being celebrated amid increased threat from Daesh militant group which has claimed a number of high-profile attacks.
In Kabul, some roads in central parts of the city were blocked by security forces.