The suspect has been identified with the help of CCTV footage, the police said.
A 51-year-old man was arrested for allegedly opening fire outside the office of BJP MP Hans Raj Hans in Delhi's Rohini area on Monday, the police said.
According to the police, Rameshwar Pehalwan, a wrestling coach at a Delhi University college for the past 23 years, fired two shots outside the office of Mr Hans.
In a CCTV footage, the man, wearing a saffron kurta and white pyjamas, was seen firing in the air outside the lawmaker's office, a senior police official said.
No one was inside the office at the time of the incident.
Rameshwar Pehalwan, a resident of Bawana, created ruckus and hurled abuses before opening fire, the official said. The accused was also drunk, he added.
According to witnesses, the man came in a car and left the spot after firing in the air.
Personal enmity appears to be the motive behind the incident and further investigations are on, Deputy Commissioner of Police (Rohini) SD Mishra said, adding the vehicle and the licensed weapon have been seized.
Hans Raj Hans termed the firing a "cowardly act" and demanded a thorough probe into the incident.
"I have no personal enmity with anyone. But I have been consistently exposing anti-people policies of the ruling party in Delhi. So it is possible that someone annoyed with this may have effected the incident," a Delhi BJP statement quoted Hans saying.
No immediate reaction was available from the ruling Aam Aadmi Party.