Bhavna Bajaj, who now lives in Ottawa, told CBC News she was pregnant when she and her husband Aman Sood applied for permanent residency in 2011.
By the time the Canadian government accepted their application last year, they had a new son, Daksh.
The couple said their immigration consultant told them to head to Canada and sponsor their son after they arrived.
But Bajaj said once they landed, they were told they had broken the law by not revealing they had a son in India.
"We are crying every day, craving for our child," Sood said.
"There's a big void in my whole life. Like, what should I do without him?" Bajaj said. "I need my kid over here ... I just want his future to be with me."
'Unjust law,' lawyer says
Lawyer RezaurRahman told CBC News that attempts to reunite the family under humanitarian and compassionate grounds have been unsuccessful.
"The immigration officer said that if the child comes here, the Canadian culture, the language, the climate will be very upsetting to him. I don't understand how one can draw such a conclusion," he said.
Rahman said that many immigrant families face similar problems in a system that allows immigration officers to use their powers arbitrarily.
"It's a bad law. It's an unjust law," he said.
Rahman said the Minister of Citizen and Immigration Chris Alexander has the power to allow Daksh to join his parents under humanitarian and compassionate grounds.
Now Bajaj and Sood are making a public plea to the minister in the hopes of making their family whole again.
CBC News contacted Alexander's office for comment on Boxing Day and has not yet received a response.Suggest a correction