Gillespie, who had been due to captain the side at Canberra's Manuka Oval, injured his shoulder playing for South Australia in Australia's domestic first-class competition and will be replaced as skipper by Cameron White.
"Obviously it's disappointing that Jason has had to pull out through injury as it would have been good to have his experience in the team," Victoria skipper White said in a statement.
Western Australia's Brett Dorey will replace Gillespie in the Prime Minister's XI with Phil Jaques stepping up as vice-captain.
