Both Tremlett (side strain) and Shahzad (hamstring strain) will undergo further assessment to determine the extent of their injuries.
Plunkett is travelling from the West Indies where he was part of the England Lions squad. The 25-year-old will arrive in Perth ahead of the final match of the seven-match Commonwealth Bank Series.
England team director Andy Flower said: “Liam Plunkett has been part of the England Performance Programme and England Lions squad this winter so we are confident that he will be ready to play a role for England should the need arise.
“We are waiting for an update on the injuries to Ajmal Shahzad and Chris Tremlett but with our preparations for the World Cup starting in less than a fortnight we need to prioritise getting our World Cup squad members fit and ready for the start of the tournament.
“We have two games left in this series and will be looking to end the tour with strong performances in Sydney and Perth.”