"I'm not in any rush. I don't want to reinjure it," Howard said.
Howard did not take part in the team's morning shoot-around. The Lakers' next game after the Nets matchup is Thursday at Boston.
Howard underwent a minor procedure Saturday in Los Angeles and did not play Sunday against Detroit, citing an inability to lift his shoulder high enough.
The Lakers will also be without Metta World Peace, suspended for a game after an in-game altercation Sunday with Detroit guard Brandon Knight.
World Peace took part in the morning shoot-around, with the Lakers finding out about the suspension afterward.
The Lakers (22-26) are 2-1 on their seven-game Grammy trip. They are only 7-16 on the road this season but hold a modest two-game road winning streak after beating Minnesota and Detroit without Howard.