The indicator rose to 5.3 percent on a seasonally adjusted basis, up from five percent in May, according to the BA federal labour agency.
Overall the number of unemployed rose by 133,000, also on a seasonally adjusted basis.
The sharp increase was due to the “extensive registration of Ukrainian refugees at job centres”, the BA said in a statement.
People escaping the conflict started by Russian President Vladimir Putin in February were now “visible” in employment statistics, BA chief, Detlef Scheele said in a statement.
Over five million Ukrainians have been registered as refugees in Europe according to the UNHCR, with hundreds of thousands finding their way to Germany.
But not all of them have found work corresponding to their qualifications, with the German language also creating a significant barrier.
Worker shortage goes up
At the same time, several sectors were facing shortages of workers, with 877,000 vacant posts, up 184,000 from the same month last year.
“Many companies are desperately seeking skilled workers,” said Fritzi Koehler-Geib, chief economist at the public lender KfW.
The shortage was particularly acute for skilled positions, Koehler-Geib said.
“This is a vulnerability of the German economy that has been building for a long time,” she said.