The biometric system, which is expected to be implemented by the end of the year, will track buyers' purchases and prevent shoppers from buying large quantities of the same product.
Opposition members, including Miranda state Governor Henrique Capriles, criticized the new program as "nothing more than a ration card."
There is also doubt that the program would be an effective tool to address food shortages, Robert Leon Parilli, president of the National Alliance of Users and Consumers, told the EFE news agency.
"We don't believe that this will be the solution to scarcity in the country, because it is a problem of local production and imports that are insufficient to meet domestic market demand... This will not be solved with fingerprint readers."
Anti-government demonstrations began in Venezuela in February, demanding an end to goods shortages, inflation and high crime.
Earlier this month, the Venezuelan government announced it was securing its 1,360 mile border with Colombia for a one-month period, from 6:00 p.m. to 5:00 a.m. local time, in an effort to crack down on the illegal export of many basic staples, including bread.