Parents attending the Stratford Children's Centre in Stratford-upon-Avon, Warwickshire, now have to have a chat and a catch-up over a plastic cup of water.
Volunteers have been ordered to change the name of the Friday morning sessions from "Coffee and Play" to just "Baby Play".
Biscuits have also been replaced by healthy snacks including fruit and bread sticks.
The weekly 90-minute sessions have been running for five years for children aged 18 months and under and no toddler has ever been injured in that time.
But last week Warwickshire County Council introduced the ban after it ruled hot drinks were a hazard to toddlers, reports the Stratford Herald.
One young mother, who did not want to be named, said: "The hot drinks were never served in a cup or a mug.
"They were served in what I regard as a 'no spill plastic safety cup' with a lid.
"They were almost like flasks, with a very small opening. Everyone is just a bit disappointed.
"I know it probably doesn't seem much, but having a cup of tea or coffee is quite a nice social thing to do as a new mum.
"Does this mean I shouldn't be drinking a cup of coffee in the comfort of my home?
"To me the ban is yet another example of health and safety madness."
Children's centres across Warwickshire can now only serve hot drinks if they are in a separate area from the toddlers.
Mum-of-two Sue Turner, 30, said: "What the council are saying is if a parent wants a cuppa they must turn their back on their child and walk across to another area of the children's centre to make it and drink it.
"Surely it is more dangerous to leave your child unattended than it is to have a cup of tea on a table next to you while you watch them."
One mother was particularly confused because she believed the existing cups they used were safe enough.
"The hot drinks were never served in a cup or mug," she said.
"They were served in what I regard as a 'no spill plastic safety cup' with a lid. They were almost like flasks, with a very small opening."
The young mother, who did not wish to be named, goes to the centre at least once a week, and she said all the mums were talking about the decision.
"Everyone is just a bit disappointed," she said. "I know it probably doesn't seem much, but having a cup of tea or coffee is quite a nice social thing to do as a new mum.
Does this mean I shouldn't be drinking a cup of coffee in the comfort of my home?
Vicky Kersey, children's centre officer at the county council, confirmed: "To minimise any risk of scalding a child we have introduced a hot drinks policy at all of the county's children's centres.
"Hot drinks can now only be served at children and baby sessions if the layout of the centre provides a separate area to consume hot drinks away from the children playing." Stratford Children's Centre will now provide water, fresh fruit and breadsticks instead of tea, coffee and biscuits.
Caroline Loveridge from Stratford Children's Centre told the Stratford Herald: "All families using the centre were informed about this change of arrangements and we invited their feedback.
"The majority of responses we have received have been positive and supportive as parents understand we want to minimise the chance of any harm being caused to their child."