Mr Cairns competes in the biathlon and swimming events as well as wheelchair basketball.
The seventh edition of the games, established by the Duke of Sussex in 2014, began in Vancouver on Saturday.
The Duke was at the opening ceremony, which had a star-studded line-up of performers including Nelly Furtado, Coldplay’s Chris Martin and Katy Perry.
More than 500 competitors from 23 nations will take part in the games, which run until 16 February.
The games aim to “inspire recovery, support rehabilitation and generate a wider understanding and respect for those who have served their country”, the Royal British Legion said.
The Invictus Games were held in London in 2014, in Orlando in 2016, Toronto in 2017, Sydney in 2018, The Hague in 2022 and Dusseldorf in 2023.
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