Mr Nicholson said Brylee was not screaming or crying but was yelling out and "just being a baby, normal baby stuff".
"If she had been crying, we would have got the pram and pushed it outside. We do that because it's unfair on people. We understand that.
"There were people there saying what a happy baby we had."
When Mr Nicholson and his wife asked why the request had been made, they were told that they weren't comforting their baby, and there were customers who wanted to have a "relaxing peaceful environment".
"I was absolutely brassed off. I was fuming to be honest. She didn't need comforting. If she was crying, we would have left.
"That someone would ask you to take a baby outside for making too much noise at a cafe at 9 o'clock in the morning - it was absolutely bizarre."
Mr Nicholson said he and his wife took Brylee to cafes in Auckland every weekend and they had never before struck any problems, either with her or his other three children.
Providores Urban Foodstore owner and chef Robin Feron said the family was asked to take their daughter outside because of the level of noise she was making. "We ask people to be respectful of all the other patrons in the place.
"It's not about the child, it's about [the parents].
"The child was [making a loud noise] over and over again for about 10 minutes. It's a natural child thing to do that. It's up to the parent to make sure the child isn't annoying other patrons."
Mr Feron, who has been in the hospitality industry for more than 20 years and run several establishments, said similar incidents happened "all the time".
"It's about the comfort of all our patrons, not just one. The patrons will walk out. Why would you walk into a place with a noisy kid if you want to sit around and talk and read the paper?
"All we are trying to do is provide a service and nice atmosphere for everyone. It's not about us kicking a 1-year-old child out."
Mr Feron said a sign posted at the cafe asked for children to be seated and supervised.
"There's an adage that 'our cafe is child-friendly as long as your child is cafe-friendly'.
"I'd like to put that up in 10ft letters. Ninety-nine per cent of parents are great."
Cafes and restaurants are within their rights to ask a party to take their child away if they are causing a disturbance, according to Consumer.
But restaurants can't refuse to let someone in just because they have a child with them.
Alan Sciascia, the Bay of Plenty regional manager for Hospitality New Zealand, said cafe proprietors faced "a careful balance" to ensure that customers weren't unnecessarily offended and affected.
"Generally cafe owners and operators are very accepting [of children and babies]. It's another part of running a business.
"There are a number of cafes that specialise and cater for children and babies; they have areas set aside [for kids].
"There are others that prefer not to cater for that. It comes down to everybody being reasonable."
Mr Sciascia advised parents visiting a new cafe to ask at the counter whether the cafe catered for children or felt comfortable with hosting children.