Bhavna Bajaj and Aman Sood made a public plea to the ministry to allow their son Daksh, who is in India, to join them in Canada.
Bajaj told CBC News she was pregnant when she and her husband applied for permanent residency in 2011. By the time the Canadian government accepted their application last year, the couple had a son.
The couple said an immigration consultant advised them to sponsor their son after they arrived in Canada but once they landed they were told they had broken the law.
A spokesman for Citizenship and Immigration Canada told CBC News on Sunday that he could not disclose information about this particular case due to privacy laws but spoke generally about the application process.
"Applicants are expected to abide by attestations they have made to officers regarding their application as they land in Canada," spokesman Kevin Menard wrote in an email. "The policy that requires applicants to disclose all of their family members in their application before landing in Canada helps CIC prevent immigration fraud and child trafficking."
He also said that applicants are expected to disclose if the circumstances in their original application change.
"In general, if someone has a baby before applying to immigrate to Canada, they are expected to disclose that," he said.
"Upon their arrival in Canada, they are expected to be forthright and truthful in their attestations — this includes any information regarding dependants. There are several stages at which people can and should divulge such information. As part of the law, any dependent that is not listed in the application at the time of becoming a permanent resident, can’t be sponsored in the future."
The couple told CBC News on Friday that they made an honest mistake when they did not disclose the pregnancy. They have asked Minister of Citizen and Immigration Chris Alexander to allow their son to come to Canada under humanitarian and compassionate grounds.
"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."