Calvin told his 11 million followers that his son was born on 20 July – adding he was “so grateful” for the new arrival.
Singer Example and Scotland footballer Andy Robertson were among the celebrities to congratulate the couple, alongside Radio 1 presenter Arielle Free, who wrote: “Welcome to the world wee Micah”.
Singer Becky Hill was among those who praised the decision to share pictures of the placenta.
“Amazing we grow a whole new organ to provide life!” she wrote.
“Good job not wasting it either, that’s some goddess magic right there!”
Others also praised the post for “normalising” the aftermath of childbirth.
But some questioned whether it was necessary to include the photo without warning, while others expressed surprise.
“I was NOT prepared for the placenta pic,” wrote one, and another replied: “Placenta and placenta pills were not on my bingo card for today but OK.”