The mother-son duo had gone to Sector 51 market to purchase some medicines when they were shot at as they stepped out of their car.
The woman has sustained bullet injuries in her chest while her son was shot in the head.
The injured were taken to a private hospital where their condition is said to be critical.
The gunman opened fire at them in the presence of a large number of people but no one came to their rescue.
The accused has been identified as Mahipal (32), a head constable, who was posted with the family for the past two years.
Later, the police managed to arrest Mahipal from Gurgaon-Faridabad road.
KK Rao, commissioner of police, said accused has been arrested and is being quizzed to ascertain the reason behind the attack.
“He (the accused cop) was under depression,” said Rao adding that he had some psychological issues.