The death toll is expected to rise.
Pakistan, a Muslim-majority nation, is observing the Islamic holy month, during which believers fast from dawn to dusk.
'Struggling for life'
Fatima Hashim, a 55-year-old witness whose daughter was seriously injured, said it had occurred in a small area where huge crowds had gathered.
"The place where wheat flour was being distributed was very narrow, which suffocated hundreds of women and children," she said.
"I went along with two of my daughters to get two bags of flour, but now my younger daughter is struggling for life in the hospital."
Another witness, Hafeeza Begum, said: "We were in a long queue waiting for our number [to be called] to get a 10kg bag of flour from the charity when people started running.
"I was quite far from the platform where the bags were being distributed, so I promptly grabbed my teenage daughter and reached a safer place."
Television footage showed images of distraught parents arriving at the Civil Hospital, women and children lying on beds and corpses covered by white sheets.
The flour handout was organised by a private group. Ahmed said that the man distributing the flour had been arrested because he had not given prior notice to the police.
Pakistan's worst stampede in recent memory, killed 29 women and children in April 2006, at a festival to commemorate the anniversary of Prophet Muhammad's birthday, in Karachi.