Under the Road Traffic Act, it is illegal for cars to carry passengers under 1.35 metres tall without a booster seat or a child restraint.
Taxis are excluded from this ruling as they are considered "public service vehicles", while private-hire car services are not.
Offenders face a fine of $120 and three demerit points.
If charged in court, they can be fined up to $1,000 or jailed up to three months.
LTA said taxis are exempt as it would be "quite unreasonable" for taxi drivers to have to turn away street-hail fares with children under 1.35 metres tall and babies.
"We are not exempting private-hire cars because they are pre-booked and passengers can indicate if they require booster seats or child restraints when making the booking," said a spokesman.
In a fatal accident last June, two young boys, who were not in child seats, were injured after their family's car crashed into a tree in Lentor Avenue.
Mr Sitoh Yih Pin, Chairman for the Government Parliamentary Committee on Transport, said that child-seat regulations for private-hire cars should be "considered and reviewed".
"The key issue here is whether (private-hire cars) should also be deemed as public service vehicles and therefore be exempt from having child seats for children under 1.35m tall," he added.
Nanyang Technological University transport consultant Gopinath Menon said there are "practical difficulties" in making child seats mandatory.
Child seats cannot be permanently installed in taxis and private-hire cars because they ferry different passengers on each trip, he said. The driver would have to keep the seat in the car boot and set it up whenever a child is among the passengers.
But National University of Singapore transport researcher Lee Der Horng said laws requiring car seats should be "universally applicable".
"There is no strong reason why taxis should be exempted from the rule. It's about safety," he said.
As more commuters use booking apps to hire taxis, operators could add an option to request car seats, he said.
Since last August, Grab has offered the option of booking GrabFamily, a six-seater car with a booster seat installed for children between the ages of four and seven.
In a blog post yesterday, Grab said it was monitoring GrabFamily and "did not rule out" introducing baby seats in the future.
In overseas markets, Uber offers UberFamily, a service that allows passengers to request a child seat. It is not currently available here.
The following article is written by Zhaki Abdullah, a Correspondent with The Straits Times.