Islamist militants on June 25 damaged a bridge providing the only road access to the town of Sebba, the administrative seat of Yagha province.
Residents swiftly tried to repair the damage but the bridge was destroyed in a subsequent attack, leaving Sebba cut off from the rest of the country.
"The food situation is critical," Sebba inhabitant Abdoulaye Ly told AFP.
"We've sounded the alarm, but at the moment we don't see the light at the time of the tunnel... people here justifiably feel abandoned."
Another Sebba resident, Mohamed Dicko, said the highway bridge was not just vital for the town but for swathes of Yagha province, including Solhan and Mansila.
Sebba, with a population of 30,000, had become a haven for many people in Yaghan who have fled their homes because of jihadist attacks.
MSF (Medecins Sans Frontieres - Doctors Without Borders) confirmed that hunger was worsening.
"There is a desperate need for food -- people are eating leaves every day," said the charity's project manager in Burkina, Ulrich Crepin Namfeibona.
"If really nothing is done to give these people food, in the coming days we could be witnessing a disaster, a nutrition crisis which will hit children most of all."
Burkina Faso first came under attack in 2015 from jihadists operating in neighbouring Mali.
Since then thousands of people have died, around two million have been displaced and more than a third of the country's territory lies outside government control, according to official figures.
Attacks have increased since the start of the year, despite a coup by colonels whose declared priority is to restore security.