The duo were killed in a neighborhood on the outskirts of the city, capital of restive Balochistan, Pakistan's largest and poorest province.
Sakina Bibi, 38, and her daughter, Rizwana, 16, had been giving drops to children when two gunmen on a motorcycle opened fire, police said.
Ayesha too sympathized with the bereaved family and while paying rich tributes to the martyrs, said "We salute all those who have given the ultimate sacrifice in this national cause, and would like to remind the nation that we will not let their sacrifice go waste; insetad, we will fulfill their dream by defeating polio in Pakistan".
Previously the polio vaccination teams used to be provided with security as well but that was withdrawn as it would attract unnecessary attention towards them, however, the recent attack might increase the need for security once again.
The incident was confirmed by senior administration official Amjad Ali Khan. More than a hundred people have been killed in such attacks since December 2012.
Man with umbrella prompts lockdown at Kirkland hospital
The hospital is going into its own lockdown procedures as police officers set up at the hospital and check for a possible suspect. Evergreen Health spokeswoman Kay Taylor said surveillance video was reviewed but it wasn't clear what the object was.
Though militants in Pakistan have been vocal against their opposition to polio vaccinations, no militant group has claimed to take responsibility of the attack.
Islamist opposition to all forms of inoculation grew after the Central Intelligence Agency organized a fake vaccination drive to help track down Al Qaeda's former leader Osama Bin Laden in Abbottabad.
Pakistan this week launched a drive against polio across the country. "Certain enemies of Pakistan do not want us to eradicate polio from our country but let me tell them that our resolve can not be defeated by such cowardly acts of terrorism", Saira asserts in the statement.
Earlier, two policemen were shot dead in a targeted attack in the Zarghoon Road area in Quetta.