The personal snapshot shows two black and white photographs side-by-side, featuring both mother and son.
It the first, makeup-free Jessica is seen cuddling up to her bright-eyed boy, who is dressed in a striped baby suit and staring intently at the camera.
The second is a close-up shot of Ace looking a little perplexed as his mum smiles in the background.
"3 MONTHS" has been written across the photographs in celebration of the milestone.
Jessica, 33, and her fiancé Eric Johnson welcomed their son on 30 June at the Cedars-Sinai Medical Center on LA.
The delighted couple are also proud parents to 17-month-old daughter Maxwell Drew.
"With two kids, we have our hands full, but every day in a new adventure," Jessica recently told US Weekly. "It's fun! I feel very at peace with being a mum."
Initially the singer has planned to keep the sex of her second baby a secret, but memorably let slip that she was having a son on Jimmy Kimmel Live back in March.
She later shared her joy at the prospect of welcoming a little boy into the family. "I'm so excited to have a son," she said at the time of her baby shower in April.
"I didn't grow up with a brother and I think the unknown is really exciting. I can't wait to have that connection with our little man."
Jessica has already showed off her slim post-baby body on a number of occasions – but it was recently revealed that she has re-signed to Weight Watchers.
The blonde beauty reportedly earned $4million in 2012 for her work with the weight loss company following her first pregnancy with daughter Maxwell.