In response, West shared images of Noah to his Instagram, captioning the post, "All in together now ... K**n baya my lord k**n baya."
The racist post appeared to have been removed and West's account would be suspended for 24 hours, meaning he could not comment on posts, share content or send messages.
If further violations occurred, the platform confirmed they might seek additional steps against West.
The rapper has been taking shots at Davidson for months - his latest being a disturbing depiction of the comedian being buried alive.
He earlier said, "I'm really concerned that SKETE [Davidson] will get my kids' mom hooked on drugs ... He's in rehab every 2 months."
It comes just three days after text messages between Davidson and West were leaked online.
The comedian appeared to call Kardashian "the best mother I've ever met", before sending West a photo of himself in bed captioned, "In bed with your wife".
Kardashian herself hit back at West over the weekend, urging him to "stop with this narrative" after he accused her of alienating him from his children.
"You were just here this morning picking up the kids for school," she wrote.
West and Kardashian share four children: North, 8, Saint, 6, Chicago, 4, and 2-year-old Psalm.