Farah was using the shorter distance to tune up for his bid at a long distance double at the London 2012 Olympics and had qualified to the final as second fastest athlete in the heats.
However, after discussion with coach Alberto Salazar, he decided to focus on racing in Helsinki.
His withdrawal is potentially good news for fellow British athletes chasing a top two finish at the trials, which could guarantee them an Olympic place, providing they have the required A standard time.
Andy Baddeley and Ross Murray have both achieved the stipulated 3:35.50 time while David Bishop, Chris O'Hare and Tom Lancashire will need to improve their season's best to stand a chance of earning the third available slot on the team.
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