The 31-year-old Farah, who won the 5,000 and 10,000 metres titles at the London Olympics and the world championships in Moscow last year, was preparing to run both distances in Glasgow.
But he said he had decided to remain at his training camp in Font Romeu in Switzerland to concentrate on being fit for next month's European Championships in Zurich.
"I have taken the tough decision to withdraw from the Commonwealth Games," Farah said in an England team statement.
"The sickness I had two weeks ago was a big setback for me.
"Training is getting better but I need another few weeks to get back to the level I was at in 2012 and 2013.
"I really wanted to add the Commonwealth titles to my Olympic and World Championships, but the event is coming a few weeks too soon for me as my body is telling me it's not ready to race yet."
England's Chef de Mission Jan Paterson added: "It is a real blow for any athlete to miss out on a major championships through injury, but to have fought so hard to regain full fitness and to have to take such a difficult decision at this stage is particularly hard.
"We wish Mo all the very best and hope to see him back to his peak very soon."
(writing by Mike Collett; editing by Ed Osmond)
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