Farah instead will run on Saturday in the 5,000 metres where he is also the London gold medallist, facing training partner and Olympic 10,000 metres silver medallist Galen Rupp.
"It's just when you are going 26 laps against the world's best you want to be at the top of your game," said organiser Tom Jordan, who added Farah was still recovering from the virus.
A less than fully fit Bekele finished fourth to Farah in the London 10,000 metres. He is now in race form, his manager said.
Kenyan 800 metres Olympic champion and world record holder David Rudisha also will miss the two-day Diamond League meeting in Eugene, Oregon, because of a leg injury discovered during an examination on Wednesday, Jordan said.
"He has a bone bruise and bruised ligaments on his knee," Jordan said.
"He tried to jog today and was limping."