Rasmussen has been ruled out of the series with a stress reaction in her ankle suffered at last week's Lion Foundation Netball Champs.
Silver Ferns coach Waimarama Taumaunu said it was disappointing not to have Rasmussen for the series, which includes Australia, South Africa and England. New Zealand's first test is against South Africa in Adelaide on Sunday.
"Grace has put in a lot of work to get back to full fitness [after recovery from ACL injury last year] and so to have another setback like this so close to the series is very disappointing for us all. For Shannon this is an exciting opportunity to expose another young New Zealand midcourter to the international stage," Taumaunu said.
Francois, who turns 22 on Friday, has yet to make her test debut. She has been a member of the New Zealand Accelerant Squad for the past two seasons.
The Silver Ferns leave for Adelaide on Thursday.
Silver Ferns Quad Series squad: Shooters: Irene van Dyk, Maria Tutaia, Cathrine Latu, Anna Thompson. Midcourt: Laura Langman (vice-captain), Shannon Francois , Bailey Mes, Kayla Cullen. Defence: Leana de Bruin, Katrina Grant, Anna Harrison, Casey Williams (captain).
