"Monta's suspension is a very serious matter to our franchise and it will be dealt with accordingly," Pacers president of basketball operations Kevin Pritchard said in a statement.
The failed drug test represents another knock for Ellis, 31, who took a step back throughout the 2016-17 season.
Over the course of 74 regular-season appearances, Ellis averaged 8.5 points in 27.0 minutes per game. Both of those marks represented the lowest since his rookie season (2005-06).
Bullock, meanwhile, averaged a career-high 4.5 points in 15.1 minutes per game during his second year with the Pistons.
However, Bullock's future with the team is uncertain entering the offseason, since the Pistons can decline his $3.3 million qualifying offer for the 2017-18 campaign and make him an unrestricted free agent.
Should Detroit choose to tender the qualifying offer, Bullock will become a restricted free agent and the Pistons will retain the right to match offer any offer sheet he receives.