It is a huge blow for the 16-time NBA champions who have failed to fire on all cylinders this season.
Howard, a three-time defensive player of the year, re-aggravated a right shoulder injury against the Denver Nuggets on Sunday and an MRI scan has revealed a torn labrum.
The center will continue to receive treatment and will be re-examined in a week.
Spanish forward Gasol, who suffered a blow to the face during the fourth quarter of Sunday's 112-105 home loss to the Nuggets, has been diagnosed with concussion and has also been ruled out indefinitely.
The Lakers are desperately trying to climb out of a 15-18 hole, having started their campaign with big hopes in the NBA after acquiring All-Stars Howard and Steve Nash during the off-season.
"Obviously it will be more difficult but no one is feeling sorry for us," Lakers head coach Mike D'Antoni said. "Other guys have to step up."
While the return of veteran point guard Nash from a leg fracture for the last seven games certainly gave the team a much needed lift, their ageing line-up has not been helped by their growing injury list and three different head coaches.
Five-time NBA champion Kobe Bryant has been their only consistent player this season and the Los Angeles have gone 10-13 since D'Antoni took over from interim coach Bernie Bickerstaff.
"It's screaming at us, isn't it," D'Antoni said after his team fell to 10-8 at home following Sunday's defeat by the Nuggets.
"We're not in a good place right now. We're losing right now because we don't have a consistent 48 minutes of basketball."