Chile says the move has no legal basis but damages bilateral relations.
Peru says residents in the new La Yarada-Los Palos district will be able to elect their representatives and take part in decisions about their future
The current row began in 2014, after the International Court of Justice gave Peru an additional area of sea.
The United Nations court gave Peru around 20,000 square kilometres (7,700 square miles) and control over a further 28,000 square kilometres (10,800 square miles) of ocean currently in international waters.
The Hague court ruling was meant to put an end to a decades-old border dispute.
The two countries disagree, however, as to where the new boundary starts.
Chile says it starts from the same point on the coastline as it does now. Peru disagrees and says it begins 270 metres inland.
The creation of the new administrative district was passed by Congress last month and signed into law by President Ollanta Humala on Saturday morning.
The Chilean government has issued a note strongly rejecting the move.
"Chile has made consistent efforts to generate a favourable climate for constructive bilateral relations.
"This move causes significant damage," read the note.
Mr Humala said the creation of the new district was part of reforms to promote decentralisation and democracy in Peru.
"It is necessary to give priority to the development of border zones and other areas of the country that have been historically neglected," he said.
The Chilean government has also accused Peru of deploying troops in the area, something Lima denies.
The La Yarada-Los Palos area has a population of about 15,000 people.
The district is in the area where where the 1879-1883 War of the Pacific took place.
The war ended in humiliating defeat for Peru and Bolivia, which lost mineral-rich land to Chile.
Bolivia lost its only outlet to the sea, and has also instituted proceedings against Chile at the ICJ.
Chile has protested against the Peruvian government's decision to create a new district in a tiny disputed border area.