The USA international played a full 90 minutes the Galaxy defeated Seattle Sounders 3-1 at the Home Depot Center on Sunday but is expected to miss the trip to take on the New England Revolution next weekend.
Arena said it was only to keep Donovan fresh after a tough World Cup campaign and not a particular injury.
"His injury is fatigue. It's not a hamstring. He's a little run down, and it showed tonight," Arena said.
"If Landon was going to play his first game back from the World Cup, it was going to be in Los Angeles. If he needs some time off, we are going to give him some time off. It may be a decision we make his week. He may not be going to New England."