The new process will affect medicines if they are likely to cost the NHS more than £20 million in any of the first three years of use.
NICE's own analysis shows that this will affect around one in five new medicines, the ABPI said.
NICE announced the price cap in March, alongside a new fast-track process for cost-effective new drugs.
If the £20m limit is likely to be exceeded, "commercial discussions" would take place between the drugs manufacturer and NHS England "to mitigate the impact on the rest of the NHS", NICE said at the time. Where a dispute arises over the cost of drugs, NHS England would be able to apply to NICE to use the drugs "in a phased way", generally for up to three years maximum, NICE said.
Drugs that deliver "a likely cost per extra year of quality-adjusted life of under £10,000" will be eligible for the fast-track process.
NICE also introduced changes to the way in which treatments for very rare conditions are considered. NICE has said that the more costly such medicines are, the "greater the health benefit it must provide" to win approval for "routine NHS use".
The ABPI believes the changes relating to products for very rare diseases are "inappropriate and unworkable", it said.
ABPI chief executive Mike Thompson, said: "These new arrangements will delay access to cost-effective medicines and deny treatments to patients suffering from rare diseases. After many months of raising concerns with NICE, NHS England and the Department of Health and offering to work constructively on alternative proposals, we have applied to formally challenge these proposals in court."
"We believe this to be the right course of action due to the potential damage these changes will cause to NHS care and on our ability to research, develop and use new medicines here in the UK. We hope that the government will reverse the changes and work with us to find a solution that works for everyone," Thompson said.
Life sciences expert Catherine Drew of Pinsent Masons, the law firm behind Out-Law.com, said: "This is an interesting approach from the ABPI and clearly it is not a step that has been taken lightly. It is apparent that those in industry, in addition to those representing patients, feel strongly that such measures will limit the access of patients to new and novel therapies and in the long term such steps could act as a disincentive to pharmaceutical companies investing in the UK. However it is also apparent that the NHS does not have an endless source of funds. If NICE concedes that its proposals are not in the best interests of patients, as the ABPI asserts, then where will the cost efficiencies that are so desperately needed be found?"