The firing incident happened in Kishangarh village late Tuesday night.
Unidentified people opened fire at the convoy of the newly elected Aam Aadmi Party legislator Naresh Yadav in Southwest Delhi when he and his supporters were returning home after visiting a temple after his victory, killing a party volunteer, police and a senior AAP leader said.
The firing incident happened in Kishangarh village late Tuesday night.
Police said they have detained a person for questioning and the incident appears to be a case of personal enmity. Sources said seven rounds were fired at the MLA's convoy.
Another person injured in the incident has been admitted to a hospital.
AAP leader Sanjay Singh identified the dead party volunteer as Ashok Mann.
"Convoy of MLA Naresh Yadav attacked in Mehrauli, Ashok Mann killed. Naresh Yadav was returning home after visiting a temple," Singh said in a tweet in Hindi.
"At least one volunteer has passed away due to bullet wounds. Another is injured," AAP tweeted.
Ankit Lal, AAP's social media in-charge, added that miscreants in another car opened fire on the MLA's convoy near Fortis Hospital.