Cardiff Metropolitan University wants to create the seven-storey facility at Queenswood - part of its Cyncoed campus.
Residents and the Woodland Trust said it would affect species including bats, birds and foxes.
The university said it had done environmental impact studies.
On Cardiff council's website, the application is listed with 133 objections, mainly from Cyncoed residents and councillors, and three petitions against it.
A spokeswoman for Cardiff Metropolitan University said it was decided to build the new accommodation as demand from students to live on-site outstrips supply.
Its plans for the 518-bed facility is on a third draft, with its position moved four times to protect the woodland, part of the campus since the original college was established in 1962.
However, the Woodland Trust has objected to Cardiff council about "damage and loss" of the "irreplaceable habitat".
The body's Heini Evans said: "Ancient woodlands support a huge array of wildlife and we need to protect these special areas."
An ancient woodland is an area that has existed continuously since 1600 or before, with these supporting more than 256 species.
But only 2% of the UK's land area is covered by them.
Resident Neil Gardner said Queenswood has mature oak trees, bluebells, protected bats, hedgehogs, foxes and many species of birds.
"As the wood is destroyed all these will be lost to the community with a considerable environmental impact on local residents," he said.
"This is an ecological and environmental crime and is intolerable to local residents."
The university spokeswoman added: "There has been lots of work to negate possible impact on wildlife including biodiversity and environmental studies.
"The university has also completed the various 'in season' studies which have been forwarded to the planning authority."
A public consultation period ended last week and council planners will meet to discuss the proposal at a later date.
Plans to build student flats on ancient woodland have been described as "an environmental crime" by campaigners opposed to the move.