The 32-year-old Namibian, who won the world 200m gold medal at the 1993 World Championships, described the decision to pull out as "one of the most difficult of my life".
He said: "I thought this would be my time to win the gold medal.
"It wasn't an easy decision to make. I wish someone would have made it for me.
"I'm very sad I can't take part, but for my health it's best not to.
"I'd like to stay and watch the younger Namibian athletes run, but it depends what the team manager decides.
Rehabilitation
"He might want me to go back home and get some rehabilitation so I am right for next season."
Fredericks said the pain in his tendon began last December during heavy training.
His doctors advised two months of rest, but when the pain did not disappear, Fredericks had a successful operation in February.
The pain returned in May, and he rested again.
Difficulties
Fredericks tried competing for the first time this year in September, but he has had difficulties when warming-up and jogging.
"I could take injections and run, but I thought I would do well by waiting until next year," he added.
"I wasn't going to run 20.5 or 20.3 just to say I've run in the Olympics.
"They could not guarantee there would be no risk and I'm not willing to take that risk."
Related to this story:
Richardson pulls out of Olympics
(09 Sep 00 | Team GB)
Johnson in injury scare
(09 Sep 00 | Athletics-Track)
Tough call over Thomas stand-in
(04 Sep 00 | Athletics-Track)