According to media reports here, Johnson complained of hamstring soreness and decided not to travel with the team for their first practice at the nets here.
If the bowler, who was slightly off-colour in the drawn third Test, fails to be match-ready, Mitchell Starc or Peter Siddle could be brought in to the side.
Johnson had already stated that he would be looking to bowl shorter spells in the last game of the series, which Australia has already won by taking a 2-0 lead.
"It depends on the fitness levels of other blokes and how they pulled up from last week. I'll always prepare to play, and I feel like the ball's coming out well from the last two BBL games, I'll keep doing the same and preparing to go. It comes back to any cricket that I play, to keep taking wickets and preparing the best I can," Starc said.
"The amount of cricket I've played with the white ball means I've got that added confidence in my game and what I want to do whether its in four overs or 10 overs," Starc said.