Just one theatre will be left open at the hospital for the most urgent cases, a source close to the pavilion said.
The move has been made as the health board struggles to cope with extreme pressure and staff shortages ahead of what is set to be the most difficult winter in history for the NHS.
NHS Lothian refused to give a date for the resumption of routine care at the eye pavilion, but did not deny reports from staff that this has been set for March 2022.
Jacquie Campbell, chief acute medical officer at NHS Lothian, said elective care had been reduced across the health board under current pressures.
"We are currently experiencing significant pressures across our health care system,” she said.
"This has meant that we have reduced our elective surgical activity across all hospitals, focusing on emergency and urgent priority patients.
"Some elective procedures are still going ahead at the Princess Alexandra Eye Pavilion (PAEP) in line with clinical prioritisation protocols.”
She added: “On occasion, staff have to be temporarily redeployed to other hospital sites to assist with staffing pressures and as dictated by clinical need.
"Since the onset of the pandemic, staff from PAEP have supported other acute sites. Similarly, should support be required at PAEP, this will be provided by the other acute sites as appropriate.”
It comes after NHS Lothian said last week it was "actively considering” a request for support from the military to cope with current pressures.
The eye pavilion has been the subject of a sustained rescue campaign after it was deemed no longer fit for purpose in 2014.
The Scottish Government agreed in principle to a replacement eye hospital next to the ERI in 2018, but this plan was later scrapped as ministers said they would not fund the project in the “foreseeable future”.
However, after public outcry First Minister Nicola Sturgeon pledged during this year’s election campaign the government would fund a new hospital after all.