Operations which have already been organised have been postponed until a later date, and no new appointments are currently being made.
It comes after a blanket decision to cancel non-urgent surgeries across NHS Lothian was taken in August.
This did not initially apply to paediatric services, but under increasing pressure these have also been postponed in recent weeks.
Urgent operations are still taking place. It is understood that some higher priority elective procedures are also going ahead.
While some health boards have cancelled operations for a set period of time, in NHS Lothian this is under constant review.
NHS Lothian said the Sick Kids hospital has seen an increased number of children sick with non-Covid respiratory illnesses, such as RSV.
These have “greatly impacted on bed capacity”, a spokesperson said.
NHS Lothian has faced increasing pressure over recent months, with concerns raised over staffing shortages.
Given the distinctive nature of paediatric nursing, NHS Lothian said staff had not been brought in from elsewhere to the Sick Kids.
But some staff from the hospital have been asked to cover the children’s ward at St John’s Hospital on occasion.
The new Sick Kids has increased capacity to deal with winter pressures, NHS Lothian said, but staff shortages due to illness have meant these cannot be used.
In response to a question from Conservative Lothian MSP Sue Webber, Nicola Sturgeon told FMQs on Thursday: “A number of health boards are taking decisions to pause temporarily elective surgery to enable them to deal with emergency services.
"That is not happening only in Scotland – we are seeing that in parts of the health service across the UK because of the pressure of Covid.
"We will continue to support the health boards to take the decisions that they consider are appropriate in order to provide care to people who need it.”
Ms Webber said: “It is deeply concerning elective surgeries are currently being postponed. That is only going to create more anxiety among patients, many of whom are lying waiting in severe pain.”