The 14-year-old girl was attacked Tuesday as she rode in her school bus. Doctors in Peshawar performed surgery Wednesday to remove a bullet from the girl's brain.
Pakistan's News International newspaper quoted a senior doctor as saying Malala was in critical condition after the surgery.
The News quoted one doctor as saying Malala had been moved to the intensive care unit of the hospital "but I am optimistic and by the grace of Allah she will recover."
Earlier, there were plans to send Malala abroad for treatment but the decision to perform the surgery at the hospital was made after Malala's brain began to swell, the News said.
A provincial official told Dawn, a Pakistani newspaper, Malala was receiving the best medical treatment available.
From the age of 11, Malala had been an ardent advocate of education, especially for girls of her age, despite the Taliban ban.
Responsibility for the attack on Malala in Mingora town in the Swat Valley in Khyber Pakhtunkhwa province was claimed by the banned Pakistani Taliban. It has been widely condemned both as Malala had won much acclaim for her anti-Taliban stand.
Various reports said Malala's attacker, after boarding her bus, sought her out by name and shot her at very close range, hitting her in the head.
The New York Times quoted a Taliban spokesman as saying Malala had "become a symbol of Western culture in the area; she was openly propagating it" and warning Taliban militants would try to kill her again if she survived.
The report quoted the Taliban also as saying they had shot he girl because she had "promoted secularism."
Two other girls were injured in the attack but their conditions weren't immediately released.
Malala's father Ziauddin Yousafzai, who used to run a school in his hometown, is a spokesman for the anti-militant Swat Qaumi Jirga.
The BBC said a reward equal to about $105,000 has been announced by Pakistani officials for information leading to the capture of those involved in the shooting.
Malik said an entire gang involved in the attack on the girl had been identified and that they would be caught and punished.
The report said there have been demonstrations in several Pakistani cities to protest the shooting.
Dawn quoted police in Mingora that several suspects, including the bus driver and the watchman of the school where Malala studied had been taken into custody.
Malala had kept a diary under an assumed named for the BBC since she was 11, chronicling the sufferings of her people under the Taliban which had taken over Swat until being driven out by Pakistan security forces in 2009.