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.
"There are no products," says Araceli Hernandez Ramirez, manager of a grocery store in Puente de Coyula.
She says she has no rice, corn or flour to sell to her customers. "They go home empty-handed," she said.
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.

The 29-year-old finished 11th in the -94kg class for Armenia, where he was born, but has since switched to represent the United States.
A retest of his 2012 sample revealed the presence of a steroid.
A total of 43 weightlifters have now failed retests from the 2008 and 2012 Olympic Games.
Six more competitors from Vardanian's event at the London Olympics are already facing disqualification after retests found steroids.
Vardanian was previously banned for six months in 2009 after testing positive for cannabis.

The so-called Islamic State group (IS) has said it carried out the attacks.
The group has established a presence in Yemen since a civil war broke out there and has carried out numerous attacks.
It is opposed to the government and Shia Houthi rebels who have seized much of the country, including the capital Sanaa.
The attacks come on the eve of the first anniversary of the Saudi Arabia-led coalition against the rebels.
Both civilians and military personnel were killed by the blasts, officials said. Dozens of others were wounded.
Two of the bombings hit checkpoints next to a base used by the coalition, they said. Gunmen then tried to attack the place.
The third explosion happened when an ambulance laden with explosives was detonated next to a military checkpoint.
No end in sight to war in Yemen
Practising medicine under fire in Yemen
The war the world forgot?
Yemen's humanitarian catastrophe
Who is fighting whom?
Meeting the Houthis and their enemies
Aden was recaptured by government troops backed by the Saudi-led coalition last year.
The campaign was launched in March 2015 in an attempt to oust the rebels from Sanaa and restore Yemen's government.
Riyadh says the Houthis, who are allied with forces linked to the former president, are supported militarily by its regional rival Iran, something it denies.
Since the offensive started, more than 6,200 people have been killed, half of them civilians, according to the UN. The war has left Yemen fragmented and facing a humanitarian crisis.
Meanwhile, IS and Al-Qaeda in the Arabian Peninsula (AQAP) have exploited the conflict to expand the territory under their control.
Mexico's air force has been flying tons of grain into Oaxaca state in the south of the country to deal with dwindling food supplies caused by roadblocks set up by protesting teachers.
[NEXT_CONCEPT]
American weightlifter Norik Vardanian has tested positive for a banned substance in a sample he gave while competing for Armenia at London 2012.
[NEXT_CONCEPT]
At least 22 people have been killed by three suicide bombings in checkpoints in the southern Yemeni city of Aden, officials say.