Kian Alexander MacKay is the couple's first child.
"Thanks to everyone for their thoughts, prayers and support. We are overjoyed with our baby boy," the Nova Scotia member of Parliament tweeted.
Afshin-Jam MacKay is an Iranian-born human rights activist, pop singer and former Miss World runner-up.
Her book, The Tale of Two Nazanins, recounts her efforts to save a 17-year-old woman from execution in Iran. She has spoken out against the ruling regime in her former homeland.
The couple married in Mexico in 2012.