The Belfast Trust said it was facing "significant pressures" with 214 children attending its A&E on Tuesday.
Nine children in the UK have died with rare but severe bacterial strep A infections since September.
A five-year-old from Belfast died from an illness linked to strep A on Monday.
Stella-Lily McCorkindale became severely ill last week and was treated at the hospital.
The trust said every aspect of the care she received was being carefully reviewed.
Cases of strep A and scarlet fever are higher than usual around the UK.
Health officials in the Republic of Ireland have confirmed that a child under five has died from Strep A infection, Irish broadcaster RTÉ reported.
The trust said postponing routine procedures had been a difficult decision but it would allow staff to care for children with serious or time-critical illnesses.
"We appreciate how difficult this will be for families and children and we apologise for the distress this may cause," a spokesperson said.
On Wednesday eight procedures were postponed, while 12 went ahead as planned.
The trust said it would be a similar pattern over the coming days, with some procedures going ahead if staff were available.
Examples of procedures that might be postponed include paediatric surgery and Ear, Nose and Throat (ENT) procedures.
The Belfast Trust said the emergency department at the children's hospital remained "extremely busy" on Wednesday night.
Consultant paediatrician Dr Ray Nethercott said postponing procedures was a disappointing but necessary step.
"This is a managed step in anticipation, so they use the resources available to them in the best way they can," he told BBC's Evening Extra programme.
"It's either that or wait for a further escalation.
"We are seeing a marked upturn in the number of viral and bacterial infections.
"This is a relatively common infection but it's occurring at the wrong time of year - not the time of year we expect to see it."
The Belfast Trust said parents should consult the online symptom checker if concerned about their child.
Pharmacies are worried about patchy supplies of antibiotics caused by the rising demand for penicillin and amoxicillin, which are used to treat cases of strep A and scarlet fever,
David McCrea, a pharmacist at Dundela Pharmacy in east Belfast, said he had run out of liquid penicillin.
"All we can say to people who come in is to try another pharmacy or ask their GP for another antibiotic, although supplies of those are running low," he said.
The Department of Health in Northern Ireland said work to maintain supplies was an "absolute priority".
A spokesperson said UK antibiotic supplies remained good but local level supply issues for some antibiotics had arisen due to a recent acute increase in demand.
The department said it was working with national counterparts to maintain the flow of supplies to Northern Ireland.
Most strep A infections are mild - a sore throat or a skin infection that can be easily treated with antibiotics.
But some people who catch it can get very sick.
Some people develop scarlet fever, which causes a skin rash (that feels like sandpaper) and flu-like symptoms, including a high temperature.
Figures show there were at least 104 cases of scarlet fever in Northern Ireland in November, up from 43 in October.
Very rarely, Strep A can cause something called invasive group A streptococcal infection or iGAS, which can be deadly.
Invasive disease happens when the bacteria get past your body's immune defences.
The government said that during a similar period in 2017-18 - the last high season for iGAS infection - there were four deaths in England.
But the number of cases of invasive group A strep, or iGAS - the most serious form of infection - is 33 so far in 2022, compared to 55 in 2018 and 72 in 2019 (before the pandemic).
The Public Health Agency said there was no indication Northern Ireland was seeing more deaths from iGAS than in previous years.
As a parent, if you feel that your child seems seriously unwell, you should trust your own judgement. Contact your GP if:
* your child is getting worse
* your child is feeding or eating much less than normal
* your child has had a dry nappy for 12 hours or more or shows other signs of dehydration
* your baby is under three months old and has a temperature of 38°C, or is older than three months and has a temperature of 39°C or higher
* your baby feels hotter than usual when you touch their back or chest, or feels sweaty
* your child is very tired or irritable
Call 999 or go to A&E if:
* your child is having difficulty breathing - you may notice grunting noises or their tummy sucking under their ribs
* there are pauses when your child breathes
* your child's skin, tongue or lips are blue
* your child is floppy and will not wake up or stay awake