On Saturday Farah said he was angry his name had "been dragged through the mud" after a BBC documentary alleged his coach Salazar and training partner Galen Rupp had violated anti-doping rules.
The 32-year-old, who won gold in the 5,000 and 10,000 metres at the London Olympics, was due to compete in a shorter 1,500 metres but has since pulled out citing the emotional and physical wear of the allegations.
"This week has been very stressful and taken a lot out of me," Farah, who was not accused of any wrongdoing by the documentary, said in statement on Sunday.
"I have not been able to focus properly on today's race and after the events of the last few days feel emotionally and physically drained.
"I want to run well in the IAAF World Athletics Championships in Beijing and have decided it is better for me to go back to the US, seek answers to my questions and get back into training.
"I apologise to the people who bought tickets to come and watch me race and ask for your understanding at this time."
(Reporting By Tom Hayward in London; editing by Sudipto ganguly)
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