The photo post, which is titled BFFS, shows the 4-week-old baby's hand grasping his 2-year-old sister North's finger. Unfortunately, the newborn's face can't be seen.
"She said, 'He's my best friend,'" Kardashian, 35, captioned the pic.
Kardashian welcomed Saint, her second child with husband Kanye West, on December 5. Click here to see all of the congratulatory gifts she's received.
As Us Weekly previously reported, Saint will likely be the couple's last child.
A source told Us in November that the Keeping Up With the Kardashians star's chances of being able to carry another baby were low due to health risks.
"It was hard for her to get pregnant, so they will feel blessed to have two happy, healthy children," the source said.
Kardashian had a low-key New Year's Eve celebration with Caitlyn Jenner and sister Kourtney Kardashian, and shared her resolutions for 2016 in a post on her website on Thursday, December 31.
"In the next coming months I'd obviously like to shed the baby weight. That's the big one to accomplish first! I'd also like to finish our home next year, so we're working hard to make decisions and meet deadlines so it gets done," she wrote, adding that she also wants to "learn how to do the splits LOL!"
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