Amazon has been singled out for adopting a leadership position on the issue
Repak says the amount of packaging waste generated in Ireland from online shopping outside the State will grow by 34% in 2018.
Ireland is now generating over 10,000 tonnes of packaging waste from online shopping per year, up from 7,500 tonnes in 2017.
This amount is the equivalent to the size Carlow would generate in packaging waste per year.
The recycling body says it costs over €500,000 a year to collect and recycle this packaging - a cost it says is "being unfairly" borne by Repak members.
It says some international online retailers are "abusing" Ireland's recycling system, by dumping over 10,000 tonnes of material.
But a new Repak Online Shopping report says Amazon is "a notable exception" - singling out other retailers such as Ali express, Missguided, Boohoo, Pretty Little Thing and Screwfix.ie.
Repak is calling for more online retailers to adopt a leadership position when it comes to paying towards the recycling of their packaging.
It says some of the world's largest online retailers place 27 tonnes of waste packaging daily on the Irish market - without paying a cent towards the nation's recycling bill.
CEO of Repak, Séamus Clancy says: "Large international online retailers are evading their packaging recycling responsibilities by dumping their packaging waste on the Irish market without paying a penny.
"Online retailers outside the state continue to use a loop hole in the law to avoid not spending a cent towards the cost of recycling the packaging they deliver to Irish households.
"The likes of Ali Express and other large online retailers will dump an estimated 10,049 tonnes on the Irish market in 2018, that's 27 tonnes per day.
"This material has to be collected, accounted for and recycled.
"It is costing €562,738 a year to collect, recycle and recover this packaging from householders, which is extremely unfair to Irish companies and Repak members who are paying to have their packaging recycled and contributing to Ireland's recycling effort.
"This must be addressed by the Department of Communications, Climate Action and Environment."
However, Repak says Amazon is showing leadership with its environmental responsibilities and is currently in the process of joining Repak to financially support the cost of recycling.
Repak is asking other online retailers to follow their example and stand up to their responsibilities.
Mr Clancy warns that online retailers based outside the State have an unfair advantage over Irish companies making contributions towards recycling and that the issue of recycling packaging from large online retailers will get dramatically worse.
"The growth rate of online shopping in Ireland is staggering and this presents a significant problem for recycling in Ireland.
"At the current rate of growth, the volume of such packaging entering the country will exceed 100,000 tonnes by 2031.
"To put these projections in context, less than 1,000,000 tonnes of packaging waste were generated from domestic sources last year.
"Currently we have no way of policing those who place this packaging on our market. It cannot continue.
"We are continually advocating that an online retail forum be established by the Department of Communications, Climate Action and Environment to consider how best to address this matter."
In 2018, Irish households will spend an estimated €2bn on online cross-border consumer goods, equating to 33 million tonnes.
Clothing/apparel, footwear and accessories are the most popular online cross-border purchases, with Irish consumers spending €386m in 2018 - which is 19% of all goods purchased online.