The German weekly says the secret service BND intercepted a conversation involving Kerry "by accident" in 2013.
The US diplomat was discussing tensions in the Middle East in a satellite link, Der Spiegel says.
Relations between Germany and the US have been deeply strained by revelations from fugitive US intelligence agent Edward Snowden last year that Washington had conducted intensive spying operations in Germany, including eavesdropping on Chancellor Angela Merkel's mobile phone.
The issue erupted again last month when two alleged German double agents working for US intelligence were unmasked.
Her government took the extraordinary step in early July of demanding that the CIA station chief in Germany leave the country, following intense pressure on Merkel to respond to what many Germans called a humiliating violation of national sovereignty.
Der Spiegel also says the BND has been spying on Turkey since 2009.
In its report to be published on Sunday, it says the German government reviews its espionage programme every four years but did not modify its priorities after the scandal over US spying.
Der Spiegel's revelations come after reports on Friday that the German secret service listened in on at least one of Hillary Clinton's telephone calls when she was US secretary of state.
The reports by three German media outlets said documents passed to the CIA by one of its moles inside German intelligence show it eavesdropped on Clinton while she was on a US government plane.
But a German government source told the three outlets that the intercept happened by accident, and only once.
According to the reports, the Clinton intercept was "not an isolated case", with the German government apparently giving permission for "spying on a NATO partner", although it was unclear which of its allies was the target.