The strike affected airports in Lisbon, the northern city of Porto, and Faro in the southern Algarve region, as well as the airport for the island of Madeira, said Acacio Pereira, a spokesman for the union representing border police.
Portugal's national carrier TAP advised passengers to arrive early at the airport and for people with electronic passports to use automated controls.
The strike, which extends to ID checks at ports and road borders, is set to continue for a second day on Monday.
Border police are protesting understaffing and salary cuts of up to 12 percent for civil servants announced as part of the debt-wracked nation's 2014 budget.
This strike is the latest in a long series of angry street protests over tough austerity policy put in place by the centre-right government to reduce its public deficit and increase the efficiency of its economy to receive rescue loans of €78 billion ($106 billion).
On Thursday thousands of striking police officers protested before parliament, warning that budget cuts would jeopardize public security.
Meanwhile in neighbouring Spain, thousands of people also turned out, demonstrating in the capital Madrid, in the southern Andalusia region and in the eastern city of Barcelona to protest severe public sector cutbacks.
People rallying in Barcelona grasped banners that read "Stop anti-social budgets" or "Cuts: enough!" as the government seeks to make further savings in a country where the unemployment rate is pushing 26 percent.
On Thursday Prime Minister Mariano Rajoy's government announced it would ease austerity reforms in the coming two years as the economy appeared to be emerging from recession.