German officials say the country will maintain stepped-up security measures until at least the end of the year.
Authorities say they have received a warning about an imminent attack.
The head of Germany's police union Rainer Wendt said police officers around the country have had their vacation leave canceled because of the heightened state of alert.
He said as long as the country's popular open-air Christmas markets, running from late November to the end of December, are in business "we must expect attacks and will protect the population with a visible presence."
Security has been increased at train stations and airports.
On Thursday, security at Namibia's international airport intercepted an unaccompanied and unidentified bag before it was loaded on a flight to Munich.
Germany has been on heightened alert since Wednesday following a tip from an unidentified foreign intelligence service about a possible attack.
Germany has been largely spared terrorist attacks by Islamist militants who have struck elsewhere in Europe in the past decade. However, analysts see the country as a potential target, in large part because of Germany's 4,600-member military presence in Afghanistan.
In recent months, Germany has said it has concrete evidence of some 70 nationals going to the Pakistan-Afghanistan border to receive militant training.
Some information for this report was provided by AFP, AP and Reuters.