The incident had taken place on Friday night.
The screening of the film "In the Name of Love-Melancholy of God's Own Country" was organised by the Global Indian Foundation and the Vivekanand Vichar Manch of JNU.
Members of the Jawaharlal Nehru University Students Union or JNUSU and the Gender Sensitisation Committee Against Sexual Harassment had disrupted the film's screening, alleging a hate campaign was being propagated in its guise.
This led to minor scuffles between the protesters and ABVP members.
The Delhi Police said it received 13 complaints from both the sides and is investigating the incident.
"We have received 13 complaints and are deliberating the ones that are actionable," said a senior police officer.
The complainants have made serious allegations, which were being probed, he said.
The JNUSU took out a march on the campus last night to protest the violence. The ABVP also took out a march titled "Save JNU from Left Lumpens" at same time.
According to the organisers, the film, directed by Sudipto Sen, focussed on the issue of "love jihad" and religious conversion of girls in Kerala. The JNUSU alleged that ABVP members attacked its former president Mohit Kumar Pandey.
ABVP member Saurabh Sharma alleged that "Mohit Pandey threatened to kill me and hurled casteist slurs. When a guard came to intervene, he sped off in his car running over another guard."
The ABVP in a statement said, "After disrupting the screening of the movie at Sabarmati dhaba, left-wing protesters grievously injured a guard intentionally."
Students opposed to the film had assembled at the Sabarmati dhaba to protest the "hate propaganda in the name of love jihad". They breached security cordons and disrupted the screening by holding placards in front of the screen.
"Why is ABVP/RSS hiding behind the Vivekanand Vichar Manch? We won't let the RSS's venomous 'Love Jihad' myth be propagated," read a statement issued by the protesters.
Former JNUSU president Geeta Kumari claimed the film "spreading communal venom and bigotry" has been screened by the Vivekananda Vichar Mach, a front organisation of the ABVP.
"JNU students standing up for gender justice and against politics of hate in the name of love jihad protested against such politics. The peaceful demonstrators were showered with eggs and stones to create a situation of chaos," she claimed.
"The JNUSU condemns these anti-social elements that have vitiated the university's atmosphere. It is reminiscent of Ramjas College, where the ABVP beat up university students," she alleged.
An effigy of the Rashtriya Swayamsevak Sangh and the ABVP was set on fire by left-wing protesters. In the scuffle, a few students got injured, while a private security guard had to be hospitalised.