The university said the cladding was used on about a quarter of the external walls at its Bainfield Halls facility.
However, it said there were non-combustible insulation materials behind the cladding, and that other fire prevention measures are in place at building where there are 30 tenants currently in residence and around 200 more summer school customers expected by the weekend.
At least 79 people are feared to have been killed in the blaze at Grenfell in west London where the polyethylene core of the material used on the exterior walls is thought to have contributed to the fire spreading so quickly in the early hours of June 14.
Cladding from 95 towers in 32 local authority areas in England have failed fire safety tests which were carried out in the aftermath of the tragedy.
However, no local authority or housing association tower blocks in Scotland have been found to use the same material.
A spokesman for Edinburgh Napier University said it had launched a review of its buildings after the Grenfell blaze.
“A physical inspection identified that around a quarter of the exterior walls on one of our buildings – Bainfield Halls of residence – featured the same cladding reportedly used at Grenfell,” he said.
“The insulation materials behind the Bainfield cladding panels are non-combustible, the panel hangings are all made of metal, the wall cavities are properly fire-stopped and the buildings are fitted with sprinklers.
“There are also a range of other fire safety measures in place, including each block having its own exit route, a modern fire alarm and smoke detection system that is tested weekly, and 24-hour on-site security.”
She added: “Work has already begun to remove and replace the cladding as a precautionary measure, and we are working closely with the Scottish Fire and Rescue Service to ensure it is safe to continue to use the building as normal. Residents are not being evacuated.”
The university intends to complete remedial work before students return for the start of the new academic year in September.
Napier University has a long-term lease on the building, which is owned by Standard Life Investments.
The Scottish Fire and Rescue Service said it was aware of the situation and is carrying out a full audit of the building.
A spokeswoman said: “We have been in close contact with the university’s fire safety adviser and our own fire safety enforcement officers will today carry out a full and thorough audit of the building.”
Edinburgh Green councillor Gavin Corbett said: “Almost as soon as the Grenfell tragedy happened I had local queries about the cladding used on the buildings at Bainfield.”
“This news will come as a great shock to the students in Bainfield and the wider community.
“It’s obviously vital that the cladding is replaced urgently and that all fire safety and prevention steps are taken in the meantime. While the fire service advice appears to be that there is no need to evacuate, if there is even a sliver of doubt I believe the university must offer alternative accommodation for those students directly affected.
“One mercy is that the flats are relatively unoccupied at the moment because of the end of term which means that work can be done as quickly as possible.
The National Union of Students Scotland called for building inspections to be extended.
President Vonnie Sandlan said: “It was encouraging to see the Scottish government announce a review of the safety of high-rise flats in Scotland following the tragic events at Grenfell Tower.
“However, in light of the worrying discovery that student halls at Edinburgh Napier University were built using the same cladding as Grenfell Tower, the remit of the government’s investigations must be extended to include educational and student accommodation buildings.
“Students live in a range of accommodation, so any review into building safety absolutely has to take into account all university, college, and private student accommodation buildings.”