"We were moving towards the Holy Family Hospital where the police had raised barricades. Suddenly, a gun-wielding man came out and opened fire. One bullet hit my friend's hand," Aamna Asif, a student of economics at the university, told PTI.
She said her friend, Shadab Farooq, a mass communication student, was injured in his left hand and taken to the AIIMS Trauma Centre.
Al-Ameen, another student, said the man was brandishing his pistol and shouted "Yeh lo azaadi (Here, take your freedom)".
There was heavy police and media presence when the incident took place.
The students were heading from Jamia to Mahatma Gandhi's memorial Rajghat. The march was stopped at the Holy Family Hospital near the university.
Students squatted in the area, asking the police to go back. As they raised slogans of "Go back, go back", police officials asked them to maintain peace and conduct their protest peacefully.
In a video, the man, wearing a black jacket and a pair of white trousers, can be seen walking on a road, brandishing a gun.
He was eventually overpowered and has been taken into custody.
The students were participating at an anti-CAA protest in the city's Jamia area.