The image was taken as the celebrity chef, 41, headed out to the Christmas Fair in London's Primrose Hill alongside wife Jools and their children.
Jools held her young son - the pair's fifth child who was born in August - in a baby harness, believed to be the popular Baby Bjorn brand, so he could see all the fun going on around him.
While hundreds of the messages left on the photo echoed the chef's sentiment, many of those who saw it also commented on the baby carrier.
celientje87 wrote: "Happy birthday. But please. Never use that carrier again. It's not ergonomic for child and can use hip dysplasia. Use a carrier that supports from knee to knee!"
Another, silwieta wrote: "Happy birthday Jools, you look wonderful, and I agree not a good choice of carrier. I know you educate about food but let others educate you about ergo carriers."
The sparring continued: silwiet posted: "Please do your research or ask your physio.
"Narrow-based carriers are not only dangerous but also uncomfortable for baby! River doesn't look particularly cosy in that pic. Should never front-face! Also hip dysphasia can be undiagnosed in 15 per cent of babies, so why take the chances?"
Georgianamatza added: "Happy birthday! But why use a non-ergonomic carrier for the baby? It's bad for his spine."
The National Childbirth Trust (NCT) offers the following advice on baby slings: "Carrying a young baby facing out is not recommended, as it forces your baby's back straight against your chest, and causes their legs to dangle in a harness like position.
"This can mean the baby's weight rests on his crotch rather than being spread from his bottom and thighs."
Childcare expert Clare Byam-Cook doubted the criticism, telling MailOnline: "If it was known to be bad for baby's hips then, quite simply, it wouldn't be on sale.
"The Olivers can afford to buy the best equipment and I'm sure they wouldn't risk their baby's health."
MailOnline has approached Baby Bjorn for comment.
