In addition, center Al Jefferson will miss at least two weeks with a sprained left ankle. Both players sustained their injuries in Sunday's win over Philadelphia.
Jackson isn't expected to play in Tuesday's pivotal game against the Miami Heat at a time when Detroit trails eighth-place Miami by 1 1/2 games for the final Eastern Conference playoff spot.
Suspended New York Knicks center Joakim Noah admitted to using an over-the-counter supplement and said the decision "backfired."
Noah was suspended 20 games for violating the NBA's anti-drug policy. The NBA said he tested positive for Selective Androgen Receptor Modulator LGD-4033 when it announced his suspension last week.
"This was a tough moment, but I'm going to learn from it," Noah told reporters. "I tried to take a supplement to help me with everything I've gone through. I've gone through a lot of injuries, and I tried to take something to help me and it backfired."
Booker became a household name when he scored 70 points in a loss to the Boston Celtics last Friday.