The 34-year-old Collingwood was hurt in Wednesday's two-wicket defeat in the sixth one-day international (ODI) in Sydney, and will fly back to England for further treatment.
However, he is expected to be fit to play in the World Cup, which begins on 19 February. The England squad flies out to the subcontinent on 12 February.
Collingwood is the sixth England player - after Ajmal Shahzad, Chris Tremlett, Graeme Swann, Tim Bresnan and Stuart Broad - to be sent home early from the Australia tour.
Australia leads the ODI series 5-1 ahead of the final game in Perth on Sunday.