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.

Ryan Beal, 20, Brandon Brown, 20, Alexandra Binns, 18, and Terrie Kirby, 16, were killed when the quad bike they were riding was hit by a Nissan 350Z.
The Nissan was taking part in a race on the A6201 Hemsworth bypass at the time.
Five people deny encouraging dangerous driving while two have admitted causing death by dangerous driving.
More stories from across Yorkshire
Prosecutor Kama Melly QC said the Nissan was one of a number of vehicles taking part in a high-speed race when the crash happened on 27 September 2015.
She told a jury at Leeds Crown Court two groups of people had travelled from Wakefield and Barnsley to use the stretch of road for racing as spectators watched from the sides of the road and a railway bridge.
Analysis of the Nissan's sat-nav showed it was doing 140mph at the time of the impact with the quad bike and had reached 144mph on previous runs along the single carriageway road, the court was told.
A passenger who witnessed the racing cars said in a statement read to the court by Miss Melly "that the scene was something like out of the film The Fast And The Furious".
The four people killed were out celebrating Miss Kirby's birthday.
The court heard a police investigation found the quad bike had no rear lights and Miss Melly said that other road users were "very concerned" with "the manner in which it was being driven earlier that night".
The prosecutor also said: "We are not saying that these defendants specifically encouraged that particular piece of driving that caused the deaths of the four on the quad bike.
"It is the Crown's case that the defendants' presence encouraged the dangerous driving that occurred over the course of the evening."
"They went knowing what they would see and participate in and went knowing that a group of supporters and enthusiasts being present would encourage the dangerous driving that did occur."
George Tomlinson, 25, of Hall Croft, Netherton, Wakefield; Nathan Jackson, 21, of Higham Common, Barnsley; Stephen Hebden, 23, of Dodworth Road, Barnsley; Lee Fisher, 29, of Pond Street, Barnsley and Bradley Lockwood, 22, of Rotherham Road, Barnsley, all deny one count of encouraging and assisting in the commission of a dangerous driving offence.
The jury was told that the driver of the Nissan, Daniel Raynor, and his front seat passenger, Matthew Todd, have admitted charges of causing death by dangerous driving.
The trial continues.
Plans to build student flats on ancient woodland have been described as "an environmental crime" by campaigners opposed to the move.
[NEXT_CONCEPT]
Four people died when their quad bike was hit by a car at 140mph as vehicles raced in scenes likened to the film The Fast And The Furious, a jury has heard.