However, insiders insist the footage shot by Jionni was tasteful and won't upset viewers, the new mother or fellow patients at the Saint Barnabas Medical Centre in New Jersey.
The source added to RadarOnline.com: "Jionni only filmed at Snooki's head though, so viewers will most likely see very little footage of the actual birth.
"Lorenzo was ready for his proud parents to show him off to the world and was filmed hours after the birth. It was done very tastefully and with respect to Snooki and other patients at the New Jersey hospital."
Meanwhile, Snooki says she isn't feeling very "glamorous" since becoming a mother.
While she's smitten with her "fabulous"little boy, she admits she's not back to her best just yet.
She tweeted: "Post birth isn't so comfy and glamorous. But my son is fabulous.
"I am SO IN LOVE with my son Lorenzo Dominic ! I had my little man last night, healthy at 6lbs! HE'S MY WORLD!'
The former party girl revealed she is already suffering from a lack of sleep but says the lack of rest is more than made up for by her son and fiancé Jionni LaVelle.
She tweeted: "Hardly any sleep but so worth it!
"Being a mum is an amazing feeling! I love my little man to death! Jionni is such a cute dad."
Jionni added: "I don't know what I enjoy more: watching my fiancee sleep or watching my son sleep. Both are amazing!"
The 24-year-old reality star has already shown off the new arrival to her co-stars including Jenni 'JWoww' Farley, who made a trip to see her at Saint Barnabas Medical Center in New Jersey.
- Bang! Showbiz