The incident took place near the residence of pro-independence Jammu and Kashmir Liberation Front (JKLF) Chairman Yasin Malik.
Hospital sources said one of the injured Yasir Hamid Sheikh, is in critical as he has received a bullet in his lower abdomen.
Local residents, however, alleged that a group of youth was playing carrom in the locality when police fired at them without any provocation.
Tension increased in Maisuma locality and its adjoining areas as angry youth took to streets chanting anti-India and pro-freedom slogans. They even threw stones at the security and burnt tyres in Lal Chowk.
As many as 64 people have died in the past 80 days since the ongoing unrest in the Valley began on Jun 11.