Parents will have to show birth certificates to prove eligibility for the new two-weekly scheme on Anglesey.
It comes into place in October, when general waste collections - which usually dispose of nappies - switch to every three weeks.
A parent said he will struggle and "not a lot of thought has gone into it".
A council spokesman said there was a separate service for older disabled children.
The local authority cited sources, including the NHS, which says 90% of children are dry most days by the age of three.
With general waste (black bin) collections switching from two to three weeks, the aim of the new service is to allow parents to dispose of nappies more quickly.
"Evidence collated by our waste management team suggests that most children are potty trained between the ages of two and three," the spokesman said.
"It has therefore been agreed to offer this new nappy collection service up until a child's third birthday."
He said requesting birth certificates will allow the council to gauge how many people were using the scheme - which will only be available from homes and not nurseries or creches.
Parents will have to get an application form from council offices and submit it along with a copy of the birth certificate.
The council currently recycles 59% of its waste, and said it will gauge the impact of the new scheme over the coming months.
Parents of children with medical conditions who are over three can apply to use a separate disposal service.
However, Ian Cheney, whose five-year-old daughter Olivia has Down's syndrome, said he just about manages with black bag collections every fortnightly.
He said when it changes to every three weeks he will "not manage" and said there was confusion over whether he was able to use a separate scheme, as the council suggested.
"For people out there in my position, what do we do?" he said.
"It is not just disabled children over three who are still in nappies. There a quite a lot of children out there.
"Not a lot of thought has gone into it."

Its assessment follows North Korea's publication of pictures showing its leader Kim Jong-un observing a missile test launch from a submarine last week.
South Korea says the test is "very serious" but that the technology is still at an "elementary stage".
North Korea has said it is developing nuclear war-heads.
Following the the launch, Mr Kim said his country now possessed a "world-level strategic weapon capable of striking and wiping out in any waters the hostile forces infringing upon [North Korea's] sovereignty and dignity", state media reported.
On Monday, South Korean Defence Ministry spokesman Kim Min-seok urged North Korea to stop developing the weapons.
"We judge North Korea's underwater test-firing of a submarine-launched ballistic missile to be very serious and a matter of concern. We urge North Korea to immediately stop developing SLBMs (submarine-launched ballistic missiles), which hinder the stability of the Korean peninsula and northeast Asia."
South Korea is taking the test launch seriously.
It and the United States are contemplating installing a missile-defence shield at huge cost, but this would be ineffective if submarine-launched missiles could get under it.
It's not clear if any missiles would be nuclear-tipped, though North Korea has said it is developing nuclear war-heads.
The submarine test indicates that it is moving faster than previously thought in its quest for potent weapons capable of striking at very short notice.
In April, a US think-tank claimed satellite pictures taken earlier this year suggest North Korea may have restarted one of its nuclear reactors.
The Institute for Science and International Security says images of the Yongbyon plant show patterns of melting snow indicating new activity.
Yongbyon's reactor was shut down in 2007 but was restarted in 2013.
A council will not offer a used-nappy collection service for children over three, saying most should be potty trained by that age.
[NEXT_CONCEPT]
The South Korean government has said that North Korea could have a submarine fleet capable of launching missiles in fewer than five years.