Acorns Nursery is due to be shut down in November – with the expected loss of 16 jobs – ahead of construction work beginning on the new Royal Hospital for Sick Children next year.
Around 125 children will now have to be placed in alternative creches as a result of the closure.
Some staff said they had already phoned several nurseries across the Lothians and failed to find any places available for their children.
The ERI nursery, run by Busy Bees, is open between 7.30am and 6pm to allow nurses and other staff on early shifts to leave their children nearby.
Acorns is adjacent to the new site for the Sick Kids hospital and clinical neurosciences department at Little France, which will be completed by 2017.
Although the land on which it stands was not earmarked for development, the owners of the Acorn Nursery decided to close the facility in anticipation of disruption from construction works.
NHS Lothian said it was the private firm that made the decision to close, but that it was already working with staff to help them find alternative nursery places.
Today, one staff member said she and many others were frustrated at the 60-day notice period given.
She said: “I dropped the wee one off and we had this letter handed to us saying the nursery would close within weeks.
“A lot of staff leave their kids there and they were devastated. It’s really hard to find places, especially at this time of year, and even harder to find somewhere which opens so early.
“People are already talking about having to take time off work to look after them and find a new place.
“We also don’t see why it was such short notice. They could have given a year or six months at least. We’ve known about the new hospital for ages.
“The staff are absolutely lovely there and they are losing their jobs as well.”
Busy Bees took over the Scotland-based Careshare Group after the decision to close had already been made.
Although NHS Lothian had not asked the nursery to move, once health chiefs were informed of the decision to close they immediately incorporated the new available land into their Sick Kids plan.
Marg Randles, managing director of Busy Bees, said it had attempted to renegotiate the closure after taking over in August but was unsuccessful.
She wrote in a letter to parents: “The extensive building works are in such close proximity to the nursery building that the disruption caused may compromise not only the children’s wellbeing but also their safety.
“We are deeply saddened and disappointed that we will not be able to realise our vision for this nursery.”
A spokeswoman for the firm added that it was working to find other jobs for staff.
She added: “We have several first-rate nurseries in the area and parents are welcome to visit these provisions to discuss their childcare requirements.”
Alan Boyter, director of human resources at NHS Lothian, said: “NHS Lothian will provide advice and support for any of our staff whose working arrangements may be affected by the closure.”