A passerby Dharampal was also injured in the incident which took place near the MLA's office in Najafgarh's Sarangpur village at around 8:30 AM, a senior police official said.
According to the official, four to five people came and opened fire at Singh, the 35-year-old MLA from Najafgarh, who suffered a bullet injury.
Dharampal, a villager who was passing through the area also, was caught in the firing and got injured.
Both were rushed to the hospital and are undergoing treatment.
"We are investigating the matter. No arrests have been made," the official said.
Singh is the brother of MCD councillor Krishan Pahalwan against whom there are several criminal cases.