In his complaint, Kamaljit's father Ranjit Singh, from the same village, alleged that his son was being harassed by his wife's family, which had led him to take the extreme step.
Police said Kamaljit, a farmer, took his son Sidakpreet Singh to his fields on Thursday, and fed him a poisonous substance and consumed the same.
While the child died on the spot, Kamaljit succumbed at PGIMER in Chandigarh.
Kamaljit's post-mortem was conducted at PGIMR and his son's post-mortem was conducted at Bassi Pathana civil hospital on Friday.
A case was registered under Section 306 (abetment of suicide) of the Indian Penal Code against Kamaljit's wife Ravneet Kaur, her father Baljit Singh, mother Charanjit Kaur and uncle Bagga Singh, all residents of Jhampur village in Fatehgarh Sahib district.
Investigating officer Kartar Singh said that Kamaljit had married Ravneet Kaur four years ago, but the couple did not enjoy cordial relations.
Police were investigating the case, he added.