The store said it had reviewed its community programme and decided to remove the facility which allows customers to buy extra items to donate.
Asda told Premier the change to policy meant it was "fair and consistent for all the charities we support" but the Trussell Trust, a Christian organisation, raised concerns.
UK Foodbank Network Director Adrian Curtis said in some areas facilities got 25% of their donations from Asda stores and the change would have a "big impact".
He said the chain had not consulted the organisation before making the decision but added it was open to talks.
"We are really, really keen to be able to talk to Asda about the some of the challenges that they're facing about permanent collection points and perhaps ways we can work with them."
Tesco, Sainsburys and Waitrose all have agreements with the Trust, he said.
"We don't have a national relationship with Asda, we do have corporate relationships with other supermarkets but unfortunately at this moment in time we don't have that relationship, so any of these collection points are arranged locally between the store and the foodbank themselves."
He added: "We know that being able to donate food to local people in crisis matters to communities, and that permanent foodbank collection points in supermarkets help ensure that foodbanks have a steady supply of food donations.
"Trussell Trust foodbanks currently have over 400 permanent collection points in Tesco stores, and over 180 in Waitrose stores, as well as some in Sainsburys' and The Coop, and these are working well for local foodbanks, which is why we'd be interested in talking to Asda."
In a statement to Premier an Asda spokesperson said: "We know we can make a huge difference to local charities and our customers and colleagues are generous when it comes to supporting their local communities, which is why we try to make sure we host a variety of good causes in our stores.
"We've recently reviewed the Asda Community programme and are investing an extra £2m into local good causes through the Asda Foundation. We're also introducing some new processes and guidelines to make it fair and consistent for all the great charities we support and to enable our Community Champions to make the best use of their time.
"Food banks are very welcome to collect donations in Asda if volunteers are on hand to explain to customers where their donations are going, which we know increases the amount of food donated."
The Trussell Trust operates more than 400 food-banks across the country, many within churches.
In 2014 figures showed more than 20 million meals were handed out by foodbanks.
Adrian Curtis speaking to Premier's Antony Bushfield: