Ratajkowski posted a picture of herself holding baby Sylvester with one arm around him, wearing matching swimwear, on her Instagram account.
Morgan, a father of four, shared the image on his Twitter account and said: “That’s not how you hold a baby @emrata – and your millions of followers shouldn’t be encouraged to do the same.
“Happy to give you some tips if you need them.”
The model, who has 26.7 million followers on Instagram, posted a series of photos with Sylvester a day before her 30th birthday with the caption: “Bday eve with the dream vacation partner.”
The first photo showed her holding her son with one arm, but later photos show her holding and hugging him with both arms.
The former Good Morning Britain presenter’s comment drew mixed reactions. Some people agreed with his criticism, while others defended Ratajkowski.
One person suggested Ratajkowski “gets advice from a qualified midwife on holding any baby”, adding: “She will find that even in this day and age supporting the baby’s head is essential to the health and safety of any young baby.”
But others pushed back against Morgan’s comments, with one person saying: “What a world we live in. Moving onto parent shaming now? Why do we have such an obsession on ‘how bad’ other people are doing with their lives. Here’s a novel idea… How about we focus on our own?”
Nicola Keaney, deputy head of trends on Twitter, commented: “Imagine mansplaining to a new mother how she should hold the child that came out of her. He’s tagged her to get a reaction to amplify his ailing profile. Not long now till he’s doing 118 adverts…”
In response, Morgan said: “If she chooses to use her baby as a prop to promote [herself] to 27 million people on Instagram, and she’s holding that baby in a dangerous way, it’s actually the duty of any caring human being to tell her so the baby comes to no harm.”
It comes a day after Morgan mocked the Duke and Duchess of Sussex over their privacy wishes, following the birth of their daughter Lilibet.
He said in a tweet he would not comment on the birth out of respect for Meghan and Harry’s “please for privacy” – but later told Australia’s Today Show that he thought the baby’s name was “ironic”.
Lilibet ‘Lili’ Diana Mountbatten-Windsor has been named after her great-grandmother, the Queen, whose family nickname is Lilibet, and the late Princess of Wales.
“You’ve got this couple who have been trashing the royal family, the monarchy, for the last few weeks and they’ve named the baby after the Queen, the head of the royal family,” he said.