The actresses will appear in 90-minute film Mary and Martha, written by Curtis and directed by The Bone Collector's Phillip Noyce.
The film is a Working Title Television production for BBC One and HBO Films, and is scheduled to air in the run up to Comic Relief in the UK in 2013.
Mary and Martha stars Swank as Mary and Blethyn as Martha, an American and an English woman who both lose sons to malaria.
Mary takes her son to Africa for a holiday where he contracts the disease, while Martha's son dies while working in Mozambique. The two women start their own campaigns to raise awareness for the illness.
Richard Curtis said of the project: "I've always wanted to write a film about the fact that when you have children, there's always the possibility of extreme joy and extreme sorrow. And over the years working with Comic Relief, I have come across the tragedy of the startling number of lives taken by malaria every year.
"This film gives me a chance to write about that too - as well as working with a team of people I hugely admire - Brenda Blethyn, Hilary Swank and the great Australian director Phillip Noyce."
Hilary Swank said: "I've long admired Phillip's work and we've been wanting to work together for years.
"When he shared with me this extraordinary story and I read Richard's beautiful script, I was inspired by the creative possibilities of working with them and Working Title to tell this remarkable journey of two women from completely different worlds who collided then forged an unbreakable friendship full of humour and grace.
"I look forward to working with them and the fantastic Brenda Blethyn on this special film."
Brenda Blethyn added: "This long overdue story of Mary & Martha is Richard Curtis at his best. A remarkable story of the courage, dignity and humour of two very different women in their effort to make the world a better place.
"I'm thrilled to be working with the wonderfully inspiring director Phillip Noyce, and to be sharing the screen with the classy and totally brilliant Hilary Swank. What more do you need to know?"
Filming for the project began last week and will take place in America and South Africa.