Wood played into second-half stoppage time of Hamburg's draw on Saturday, after which the German club wished him well on his travels, but U.S. Soccer said he has a back injury.
On Monday, Hamburg said Wood "is laboring with severe pain in the area around the lower back" and is receiving intensive treatment from their medical department.
The U.S. opens camp in San Jose, California, on Monday. The team plays its first qualifier since rehiring Bruce Arena as coach against Honduras in San Jose on Friday, then travels to Panama for another game four days later.
Wood, 24, was likely in line to start for the U.S. alongside Jozy Altidore as the U.S. looks to overcome November's two opening defeats in the final round of CONCACAF qualifying.
The addition of the New York Red Bulls' Kljestan -- who became the second player in MLS history to record 20 assists in a season last year -- rather than another striker suggests the injury to Wood may have altered Arena's formation plans.
Sporting Kansas City's Besler will bolster a back line that is already without the injured DeAndre Yedlin and Eric Lichaj. Hertha Berlin cleared defender John Brooks to join the U.S. despite a minor knee injury.
Last week, midfielder Fabian Johnson had to pull out of the squad and was replaced by Graham Zusi, while goalkeeper David Bingham is in for Brad Guzan.
Jordan Morris, another forward, fell awkwardly on an already sore ankle for the Seattle Sounders on Sunday but stayed in the game. He said afterward that he didn't think the ankle was going to be a major issue.
"I sprained it in preseason a little bit and it's the same ankle but I could play 60 minutes on it or whatever so that's promising," Morris said. "I'll get it looked at down there but I think it will be fine."
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