A suspicious package containing a detonator, batteries and a ticking clock was found on a suitcase which could have been bound for Munich, German police have said.
The bag was detected during screening at the main international airport in Namibia's capital Windhoek.
The incident led a Munich-bound flight to be delayed for several hours.
On Wednesday, Germany boosted security amid intelligence pointing to a planned terror attack.
It is not known if the latest discovery was part of this attack, says the BBC's Stephen Evans in Berlin.
But Interior Minister Thomas de Maiziere said the package was likely to have been bound for Germany.
"There is a lot of evidence that the luggage was intended to be transported on the flight to Munich, but we will know more about the details in the coming few days," he said.
The German Federal Crime Office (BKA) is sending experts to the Namibian capital, Windhoek, to examine the package.
It was detected at the luggage screening point prior to loading, said the Namibia Airports Company (NAC).
"We are still investigating the suspicious object," a Namibian police spokesman told the BBC. "It's too early to say if it's terrorist-related. We will only pronounce when the investigation is completed."
Further security checks were carried out on passengers, luggage and the plane itself before the LTU/Air Berlin flight was allowed to depart.
No explosives were found in the bag, Air Berlin said.
Nor was it clear whether the package was intended for Germany, as there was no destination sticker on the piece of luggage, a spokeswoman said.
All passengers had to identify their own bags before they were reloaded.
However, cargo due to be loaded on the flight was kept back for further investigation, said a statement from NAC.
Mr de Maiziere appealed for calm: "International terrorism would like to spread fear and horror in our country. We will not allow this."
He rejected suggestions that data retention laws should be strengthened to allow the authorities to store more information from e-mails and phone calls.
On Wednesday, Mr de Maiziere said Germany would be stepping up security at airports and railway stations in light of "concrete indications" of terrorist attacks being planned for the end of November.
Borders would also be more tightly controlled.
The German authorities remain fearful about the current whereabouts of a group of Islamist militants who disappeared from a Hamburg mosque a year ago, some to turn up in training camps in northern Pakistan and Afghanistan.
Call for vigilance
Mr de Maiziere said Germany had received a tip-off after two parcel bombs were intercepted en route from Yemen to the United States last month.
One of the parcel bombs went through the German city of Cologne before it was detected in the UK.
German interior ministers from federal and state governments met on Thursday in Hamburg to discuss the elevated threat.
There were "concrete indications" that Berlin, Munich, Hamburg and the Ruhr Valley were the likely targets of terrorist attacks, said the interior minister of Rheinland-Pfalz, Karl Peter Bruch.
"We are forearmed," he said, speaking on SWR radio.
A state senator in Berlin has called on people to remain vigilant and notify the authorities if they see anything suspicious.
"When we see something in the neighbourhood, say three peculiar-looking people move in who do not allow their faces to be seen, and who speak only Arabic or another foreign language that we do not understand, then people should have a look and tell the authorities what is going on," said Ehrhart Koerting, speaking on regional radio in Berlin.
Security fences have been put up around the German parliament, the Reichstag. Extra security measures are also in place around Jewish sites in the capital.