Organisers asked fans at the three-day event to leave calmly "in order to help police investigations" but said they were hopeful the festival would resume on Saturday.
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The three-day "Rock am Ring," held at the famous Nuerburgring sports complex near the western city of Nuerburg, is scheduled to run until Sunday. It draws tens of thousands of people annually.
In a statement, police in the city of Coblenz said they were in possession of "concrete elements, in the light of which a possible terrorist threat cannot be ruled out."
"As safety is the key priority and any danger to festivalgoers has to be avoided as much as possible, a decision has been taken to suspend the festival for today," the statement said. There were no further details.
Security for the festival had already been stepped up, with an additional 1,200 staff, in response to the May 22 Manchester bombing which occurred after a concert by US singer Ariana Grande.
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Last year's Rock am Ring programme was curtailed by violent storms in which dozens of people were injured by lightning.
The country remains on high alert after an attack on a Christmas market in Berlin on December 19. Anis Amri, a 24-year-old Tunisian, hijacked a truck, killed its Polish driver and ploughed the vehicle through the market, claiming 11 more lives and wounding dozens.
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