Manpreet Aulakh sustained bullet injury and has been admitted to government hospital in sector 16, they said.
Police said some students belonging to Panjab University Students' Union (PUSU) and Students' Organisation of India, students' wing of Punjab's ruling Shiromani Akali Dal, engaged in an argument over some issue which led to the clash at about 8 PM.
Shots were also fired by some unidentified persons and one bullet hit Aulakh, who is from SOI, in his thigh, DSP Central Satish Kumar said.
Two vehicles were damaged by some miscreants, he said.