Zoona was shot on Saturday evening in the neck by suspected militants inside her house at Hardshiva Sopore in north Kashmir's Baramulla district, 52 kms from Srinagar.
She is undergoing treatment at the intensive care unit of a hospital. This was the second attack in as many days on panchayat members in the state.
Militants had earlier shot dead sarpanch Habibullah Mir in Sopore.
Ramzan said the prime concern of the family was to save Zoona's life and added they did not have any demands from the government "as such".
"Right now, all we are concerned about is her health... to save her first. She is in a critical condition. Her one eye is completely damaged. We do not seek anything from the government as such but if it can help us, it is welcome to and should come forward," he said.
In the wake of similar attacks last year, many panchs and sarpanchs had demanded security from the government. The fresh round of attacks has led to calls for security again.