The protest by the student wing of the Jamaat-e-Islami religious party was one of several staged across Pakistan by Islamist groups after Friday prayers against the French magazine's depiction of the Prophet Muhammad.
Hassan was stable and conscious after the bullet entered his back and exited through his chest via a lung, medics at the Aga Khan University Hospital and relatives said.
Police and witnesses at the scene blamed the protesters for the violence, saying they opened fire on the police when they were blocked from reaching the consulate.
Two others, a policeman and a local TV cameraman, received minor wounds and were discharged from hospital after first aid.
Hassan, 38, has worked for AFP since 2005, mainly from the sprawling port city of 18 million people.
The New York-based Committee to Protect Journalists demanded the culprits behind Friday's incident be brought to justice.
"We call on authorities to quickly and thoroughly investigate the shooting of Agence France-Presse photographer Asif Hassan and to hold the perpetrators to account," said Bob Dietz, CPJ's Asia programme coordinator.
"Journalists in Pakistan must be able to safely cover newsworthy events."
Fourteen journalists in Pakistan died in 2014, according to the International Federation of Journalism, making it the deadliest country in the world for the profession.
Protests against Charlie Hebdo, which published a new cartoon of the Prophet Muhammad a week after 12 people were killed at its offices by Islamist gunmen, also shook other parts of the Muslim world on Friday.
Four people were killed and 45 injured in protests in Niger's second city of Zinder that turned violent with demonstrators ransacking three churches and torching the French cultural centre.
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