The couple, who tied the knot in secret in June 2014, managed to keep the pregnancy and birth completely under wraps.
A representative for the actress confirmed to People that Alexis gave birth last autumn, but the news has only just come to light.
Vincent Kartheiser and Alexis Bledel welcomed a son last year
Her co-star Scott Paterson, who plays Luke Danes on the show, spilled the beans in an interview with Glamour. Scott spoke about he and Alexis were "comparing notes" about their children when they returned to set.
"It was great to see her," said Scott. "She's really blossomed as a woman and now she's a proud new mother and married and happy. She's just the most likable, intelligent person and adorable human being. She hasn't changed at all. She looks the same.
"We're comparing notes because my son is about a year and a half older than her young son. I'm showing her photos and videos and what to expect. We're just really enjoying each other's company."
The actress kept her pregnancy under wraps
Alexis and her husband Vincent met on the set of Mad Men, when the 34-year-old actress played a cameo role on the show as Vincent's love interest.
Romance blossomed off-set but it wasn't until the series wrapped that the pair started dating. A source told People: "Vinnie basically fell in love with Alexis while she filmed a three-episode cameo. He was definitely smitten with her from the beginning."
It was her co-star Scott Patterson who spilled the beans
The couple confirmed that they were an item in October 2012, when they stepped out to a photography event together in New York City.
Five months later, Vincent popped the question with a stunning, vintage engagement ring. The lovebirds said "I do" in a top-secret California wedding in June 2014.