The airport manager, AENA, tweeted that 26 flights had been diverted to other airports by the time air traffic restrictions were lifted at 14.15 p.m. (1315 GMT). It said that a security committee had been set up to study the incident.
Spain's Civil Guard said an investigation had been opened after two pilots had reported seeing some drones near the airport, which is located just east of the city center.
Enaire, which activated a special procedure to halt landings and takeoffs and diverting flights to other airports, warned in a tweet: “A drone is not a toy, it's an aircraft."
With an average of 1,200 flights per day, the Adolfo Suárez-Barajas international airport in northeastern Madrid is the one with most traffic in Spain and one of the busiest in Europe. Nearly 62 million passengers went through the airport last year, AENA said.
At the end of 2018, more than 140,000 travelers were stranded or delayed after dozens of drone sightings shut down London's Gatwick airport, Britain's second-busiest, for parts of three consecutive days.