Similar to other airports strategically placed on the coast of Brazil, Afonso Pena, was built by the Brazilian Air Force Ministry in partnership with the United States Army during the Second World War. However, since its construction was completed only in 1945, shortly before the end of the war, Afonso Pena never saw heavy military movement. On January 24, 1946, it was dedicated as a civil airport.

The original passenger terminal was in use until 1959 when a new terminal was built. This terminal is used until 1996 when the much larger terminal opened. After the new terminal opened, the older terminal became a cargo terminal.

The unstable weather conditions of the region are the main problem with the airport, particularly fog and smog in the morning hours of winter and the fact that the auxiliary runway 11/29 is too small and plagued with old equipment. There are also plans to upgrade runway 15/33 from an ILS CAT II runway to ILS CAT III.

Since the bottleneck for the airport is the cargo capacity, the main runway was lengthened in 2008 to allow cargo flights to operate with greater loads and the cargo terminal was upgraded.

On 31 August 2009, Infraero unveiled a BRL30 million (USD16 million; EUR11 million) investment plan to upgrade Afonso Pena International Airport focusing on the preparations for the 2014 FIFA World Cup which were held in Brazil, Curitiba being one of the venue cities. The investment included the enlargement of the apron and implementation of taxiways. The terminal is 45,000 m2, has 14 jetways, and is capable of handling 15 million passengers annually. There are 800 parking places. The airport complex includes a small museum, a playcenter and a mall with 60 stores inside the main terminal.

Responding to critiques to the situation of its airports, on May 18, 2011, Infraero released a list evaluating some of its most important airports according to its saturation levels. According to the list, Curitiba was considered to be requiring attention, operating between 70% and 85% of its capacity. American Airlines launched service to Miami in November 2013. The outbound flight operated via Porto Alegre, while the inbound one was nonstop. The carrier terminated the route in February 2016.

Previously operated by Infraero, on April 7, 2021, CCR won a 30-year concession to operate the airport. On April 26, 2025 CCR was rebranded as Motiva.

On November 18, 2025 the entire airports portfolio of Motiva was sold to the Mexican airport operator ASUR. Motiva will cease to operate airports. The transaction was completed on August 31, 2026.