Frank is planning a publicity campaign around a ‘visually stunning', high-profile event. Further details are undisclosed.
The charity wants to win coverage in national media to target the general public, with a particular focus on the under-30s.
It is the first time the charity has used an agency to promote the week, which head of media and public affairs Leigh Daynes described as ‘a landmark week in our fundraising calendar'.
The consumer agency's brief is to help the Red Cross's fundraising activity stand out from that of other organisations.
Frank chairman Graham Goodkind said: ‘The British Red Cross Appeal Week hasn't perhaps got the prominence that it deserves, and we aim to change that for 2007'.
The campaign will attempt to highlight the fact that, while the British Red Cross is well known for its emergency response to major disasters - such as the 2005 Pakistan earthquake and the Boxing Day tsunami in 2004 - it also does a great deal of its work on British soil.
The British Red Cross generated around £1m during this year's Appeal Week, a figure it hopes to beat next year.
‘We recognise the added value that a relatively modest investment with Frank will have in extending the Appeal Week's reach,' said Daynes, adding that the agency had been selected owing to its ‘simple and compelling' ideas.
Frank saw off two other agencies to land the account.