Howard, a three-time defensive player of the year, aggravated a right shoulder injury in Wednesday's game against the Suns in Phoenix and has returned to Los Angeles for further treatment.
"His status for Sunday's game against the (Detroit) Pistons and the remainder of the team's road trip is day-to-day," the Lakers said in a statement.
Howard missed three games last month because of a torn labrum in his right shoulder, his injury woes coming at the worst possible time for the crumbling Lakers.
Los Angeles has fallen to 20-26 on the season, currently well out of the playoff race and in a whirlwind of trade rumors and team dysfunction.
In Howard's absence, Spanish forward Pau Gasol will come off the bench into the Lakers starting lineup against Minnesota.