In Schumer's snap, Fischer stood with his son cuddled up on his shoulder, with the newborn's tiny head turned towards the camera.
"Gene Attell Fischer And his dad Chris," Schumer captioned the image.
The comedian received plenty of congratulatory comments from her famous friends, including Glenn Close, who wrote, "Congratulations, Amy! YOU DID IT! He is gorgeous. Sending love."
Ben Platt was clearly a fan of the baby's name, writing, "GENE!!!!!!!!"
"beauty boy and perfect best name," chimed in Lena Dunham, with Debra Messing adding, "Oh my God he's so beautiful. Look at his eyes.... congratulations Mama! I'm so happy for you all!"
Juliette Lewis, Andy Cohen, Emily Ratajkowski, Nina Dobrev, Nicole Polizzi, Kate Walsh, Laura Dern, Amber Rose, Colleen Ballinger, Michelle Wolf, Kathy Griffin and more stars also offered congratulations to the family.
Schumer originally announced baby Gene's birth with a snap of herself holding her son in a hospital bed as Fischer planted a kiss on her forehead.
Schumer announced her pregnancy in October, shortly after Markle, and joked that the two would be competing throughout their pregnancies.
"Chris and I are thrilled and almost positive he's the father," she told the Los Angeles Times. "I look forward to competing with Markle every step of the way."
Schumer gave birth on Sunday, May 5, one day before Markle and Harry welcomed their son.
The comedian has been open with fans about her difficult pregnancy, which saw her suffer from Hyperemesis gravidarum.
In February, she was forced to cancel several shows on her tour, saying at the time, "The baby and I are healthy and everything looks good. But I am in my third trimester and I am still nauseous all the time and vomiting. I vomit mostly every time I ride in a car even for five minutes."0comments
"I have a pretty good attitude about it and some days I feel good for a couple hours. But mostly it's sucks. I wanted to push through and do my shows," she added. "I hate letting people down and I love stand up and money! But more than that I have to think about my health and the baby."
Photo Credit: Getty / Kevin Mazur