The reality star posted the snap on her website to mark her late dad's birthday.
"Today is my dad's birthday," she wrote. "I know there's nothing more in the world he would have wanted than to meet his grandchildren.
"So I wanted to share this pic of Saint with you all."
The 35-year-old gave birth to her second child with husband Kanye West on 5 December 2015.
The celebrity couple revealed they had named their newborn son Saint two days later and received a very mixed reaction.
The mum-of-two has previously given fans teasers about what Saint looks like through her app.
"He’s so cute, you guys, you have no idea," she said during a live stream. "He looks kinda like just like me, don’t you think?
"He’s so cute – he looks just like me!"
Kardashian's dad, Robert Kardashian, died on 30 September 2003 of oesophageal cancer, aged 59.