Last month, incumbent James Bond received his first child with his wife Rachel Weisz, a girl.
The family is based in New York City and Craig was discovered in a place with his daughter in the East Village a couple of days ago.
With a sports kit, a baseball cap and glasses not to attract attention, the 50-year-old boy had his daughter tied with a papoose.
However, Morgan, of Good Morning Britain, decided to comment this negatively.
Yesterday morning he tweeted: "Oh 007 … you do not too?! #Papoose #emasculatedBond".
But apart from a series of proud dads who share pictures of themselves using the children's bag, several celebrities have come out against Morgan.
This includes Captain America's star, Chris Evans, who replied: "You really have to be so unsure of your own masculinity to worry about how another man carries his son.
"Any man who wastes time quantifying masculinity is terrified inside."
Morgan has been hit by a Twitter storm that he labeled "Papoose-gate."
The television host has even introduced himself as the next Bond with a picture of himself in a dinner jacket.
He tweeted: "One thing is clear after the fierce Papoose-gate debate tonight: we need a new James Bond.
"A 007 that looks good in a tuxedo and will not be seen dead in a papoose …"