The paper straws will be sourced from suppliers in Northern Ireland and Wales.
The move comes after the Government proposed a ban on plastic straws and cotton buds in England in April. But it could take years to come into effect.
Several large United Kingdom restaurant chains such as Pizza Express and Wagamama have already stopped using plastic straws.
UK Environment Secretary Michael Gove called on other companies to follow the example of McDonald's. And in Malaysia, McDonald's will try a new approach to dispensing straws - giving them out only if a customer requests one.
While plastic straws are technically recyclable, their small size and weight mean they are often missed by sorting machines and the sheer number of straws used every day means they make a big contribution to the millions of tons of plastic that end up in our oceans every year. Pizza Express said it would replace all plastic straws with biodegradable ones by summer 2018.
However, not everyone favoured plastic straw ban. Only 1% are recycled, largely because they are made of a mixture of polypropylene and polystyrene.
Kylian Mbappe breaks silence on injury scare ahead of World Cup
Despite all their talent, Les Bleus have struggled for consistency and often appeared vulnerable in World Cup qualifying. The 2018 FIFA World Cup will last till July 15, with the games set to be played at 12 stadiums across 11 Russian cities.
The move by McDonald's comes as plastic waste has come under fire globally, particularly for contributing to ocean pollution and harming birds and sea mammals.
But not everyone thinks total bans are the answer.
Speaking in March, Paul Pomroy, McDonald's UK CEO, said "the reduction and use of plastics is a hugely important issue - for our business, for the sector and for society".
Campaigners, such Michaela Hollywood who has spinal muscular atrophy, have urged companies to ensure they are providing alternatives to plastic straws as opposed to an all-out ban, as some disabled people rely on straws in order to be able to drink.
McDonald's is preparing to test plastic straw alternatives in the United States later this year, the fast-food giant announced on Friday.
McDonald's will use two companies to meet their needs, according to RTÉ - Huhtamaki, which has a production plant in Belfast, and Welsh start-up Transcend Packaging.