Officials say 108 tons of corn will be delivered by the end of the weekend.
Last month, eight people were killed in Oaxaca in clashes between the demonstrators and police.
The protesters oppose reforms that allow the federal authorities to remove teachers who fail evaluation exams.
Members of the CNTE union, which has a history of radical activism, have been blocking roads in Oaxaca and other states ever since the union leaders were arrested in early June.
The roadblocks have prevented food deliveries to some remote areas in the region, the government says.
In a strongly worded message on Friday, Interior Minister Miguel Angel Osorio Chong said the unrest had hurt millions of people and “the blockades and damages to the citizenry must end”.
“The time is up,” he said, warning that “the necessary decisions will soon be taken to allow transit on strategic roads”.
The CNTE union opposes education reforms introduced by President Enrique Pena Nieto in 2013.
The changes include new measures to assess teachers’ performance.