The first courts will start operating near the Hungarian villages of Roszke and Asotthalom close to the border with Serbia.
Last week, the Hungarian government adopted a new package of laws on tackling the refugee crisis, due to come into force on Tuesday.
The law stipulates detention or deportation for illegally crossing the border or damaging the border fence. The legislation also envisages tougher punishments for human traffickers.
The European Union has been beset by a refugee crisis, with thousands of undocumented migrants arriving in EU member states, fleeing violence and poverty in their home countries. Many of them use Hungary as a transit point on their journey to wealthier EU states where they intend to apply for asylum.
Budapest estimates that some 172,000 refugees and migrants have entered the country since the beginning of 2015.