The incident took place around midnight at B R Vatika in southwest Delhi.
Though sources claimed that the incident was related to celebratory firing, police said it occurred during a quarrel.
The police said that a PCR call was received about a quarrel and firing at B R Vatika near the Sherpur Main Road Chowk around midnight.
Constable Naeem, posted with the Special Cell, allegedly fired three rounds from a police pistol during the marriage function, Deputy Commissioner of Police (DCP), North East, A K Singla, said.
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The DCP said another call was received by the police regarding a "quarrel" and snatching of Assistant Sub-Inspector (ASI) Irtkhab Alam's service pistol.
Alam is also an officer of the Special Cell.
However, police found that the ASI's pistol was taken for firing by Naeem.
The pistol used for firing has been seized, and a search launched to nab the accused constable, he said.
The Special Cell policemen were guests at the marriage function. Following the incident, people chased them. Though Naeem escaped, Alam was caught and thrashed, the DCP said.
Police have registered a case against the accused under charges of attempt to murder, causing hurt and endangering life of others at Khajuri Khas police station and also under provisions of the Arms Act.
The role of the Special Cell ASI is also under the scanner, police said.