It is not known why Rashida and Ezra have yet to confirm they welcomed their child.
Their reps have not returned calls to DailyMail.com.
In March Rashida showed off her bump in a pink dress at the Vanity Fair Oscar party in Beverly Hills.
In 2014 she said she was fine with not having kids.
'My life's great! But it's just this weird thing that's been hammered into my head culturally: that's the only way to succeed, that's the only thing that counts for a woman,' she said at the time.
'I'm happy, but the fact that I'm not married and don't have kids — it's taken me a long time to get to a place where I actually am OK with that, where I actually don't feel like I'm some sort of loser.'
She was previously engaged to Mark Ronson and has dated John Krasinski, Colin Jost and Jon Favreau.