BERLIN—Germany’s BND foreign intelligence service suffered damaging leaks this week, literally.

The theft of water faucets on several floors of the agency’s future Berlin headquarters—now a sprawling construction site at the heart of the capital—caused extensive flooding in a building on Tuesday, causing heavy damage, the police said late Wednesday.

Beyond prompting widespread hilarity on social media, the incident raised serious concern that what Berliners have long dubbed the Republic’s best-protected construction site may be nothing of the sort.

German officials familiar with the incident said they doubted the perpetrators’ purpose was to obtain a small number of water taps worth less than €100 ($111) apiece, suggesting their goal could have been sabotage, or even espionage.

“If water faucets can be dismantled unnoticed, one wonders what else can be installed unnoticed,” wrote Konstantin von Notz, a lawmaker and intelligence-service expert with the opposition Greens, on his Twitter account, alluding to taps of a different sort.