First Lady Michelle Obama started the garden on the White House south lawn in 2009, the first time vegetables had been grown there since Eleanor Roosevelt's "victory garden" during World War Two.
She uses the garden as a vehicle to talk about healthy eating and reducing childhood obesity. Some of the produce is used at the White House, while much is donated to a local soup kitchen.
White House gardeners are allowed only to water the plots and cannot harvest the vegetables.
White House staff who normally volunteer to pick the weeds are off on furlough, Gehman Kohan said.
"Pounds and pounds of ripe organic bounty have gone to waste," she wrote.
"Weeds are springing up everywhere, and the vegetables that have already fallen off the vines are now mouldering on the ground,"she said.