
Jankovic, third in the world, withdrew several hours before before her scheduled evening start against Serena Williams in the final to decide the title at the eight-nation, mixed team event.
Under the rules, though, should Djokovic beat Fish, then the tie would go to deciding mixed doubles, locked at 1-1 with the winner of the mixed triumphing.
That scenario has worked twice in the last two days for the Serbs, who could lift the mixed and their first-ever trophy.
Jankovic hurt herself lunging for a shot on Wednesday and was unable to finish singles matches over the past two days.
Should Fish win the singles out of the box, the US would claim a fifth trophy in Perth on an unbeatable 2-0 scoreline.
Tournament doctor Hamish Osborne said that Jankovic would not be capable of playing two matches, especially given the need for treatment after any singes.
"The treatment she has been receiving has been painful and she will be far better off preparing for the doubles, which is less strenuous."
As a consolation for a sellout crowd at the Burswood Dome, tournament director Paul McNamee and VIP guest Martina Navratilova will reprise their 1985 Wimbledon-winning mixed doubles combination in a pro-set exhibition at the end of the final.