The agency won the brief following a five-way pitch.
Palm PR will support the business, based in Northern Ireland, expand across the UK with a consumer and trade media brief to raise awareness of the brand.
The campaign will include reviews in food and drink publications and securing testimony and endorsements from journalists and bloggers.
Liam Keogh, Palm PR director, said: "Mash Direct's expansion into Great Britain through its partnership with Asda represents an exciting period of growth for the company.
"By working with both trade and consumer media, the agency will significantly increase consumer awareness of the brand's award-winning product range. The team will drive reviews and endorsement in the press, delivering a campaign that actively aids sales with this new retailer and all stockists in Britain as the business seeks to expand trade here."