The BKA said the suspicious baggage had been seized Wednesday at the international airport in Windhoek before it was loaded on to an LTU/Air Berlin flight to Munich.
"A subsequent x-ray (of the luggage) revealed batteries that were attached with wires to a detonator and a ticking clock," it said in a statement.
"Only the ongoing forensic investigation will show whether this was a live explosive."
Passengers on the flight as well as all luggage in the hold and the aircraft itself underwent subsequent checks before the plane was given clearance to take off.
"They arrived in Munich safe and sound last night," the statement said.
The BKA said it dispatched officers in South Africa to Namibia, a former German colony, to aid in the investigation and planned to send further experts to examine the suspected bomb.
The German government hiked security measures at rail stations, airports and other public spaces Wednesday following a tip-off from a "foreign partner" about an attack by militants planned this month.
"Since the middle of 2010, the security services have noticed increased indications that the terrorist organisation al Qaeda has been planning attacks in the United States, in Europe and in Germany," Interior Minister Thomas de Maiziere said.
Citing security sources, the Tagesspiegel daily reported Thursday that the United States had told Berlin that between two and four al Qaeda operatives were on their way to Germany and Britain to attempt attacks.
Among the targets Tagesspiegel cited were Germany's popular Christmas markets. The paper added the militants were expected to arrive in Germany on November 22 via India or the United Arab Emirates.
Last month authorities discovered two US-bound parcel bombs originating from Yemen, one of which went through Cologne airport in western Germany.
And on November 2, an explosive device arrived by post at Chancellor Angela Merkel's office in what De Maiziere said was likely a suspected attack by Greek radicals.
The head of Germany's police union, Konrad Freiberg, warned Thursday there were "security deficits" in Germany and that the country was underprepared for a terrorist attack.
"We have missed a few steps along the way and there are security deficits that we have drawn attention to," he told the Hamburger Abendblatt daily.
German police warn of 'security deficits' after attack tip
The head of Germany's police union warned on Thursday there were "security deficits" in the country, after the government said it had learned an attack was being planned for the end of the month.
Konrad Freiberg said Germany was underprepared for a terrorist attack. "We have missed a few steps along the way and there are security deficits that we have drawn attention to," he told the Hamburger Abendblatt daily.
Describing the situation as "serious", Freiberg said: "We need to do everything possible to protect the public from danger."
On Wednesday, De Maiziere ordered security beefed up across the country, after receiving a tip-off that an attack was being planned in Germany for the end of November.
"There is reason for concern, but no reason for hysteria," said the minister at a hastily convened press conference.
He said the security situation was similar to that before Germany's last general election in 2009, but the interior minister of the city-state of Berlin said the position was worse.
There is "a clearly more tense situation" than before the election, said Ehrhart Koerting.
The chief of the federal police, Matthias Seeger, said: "We assume that the current security level is a step higher than it was before the election," adding there was "no reason for panic."
Meanwhile, the interior minister of the southwestern state of Rhineland-Palatinate, Karl Peter Bruch, said there were "concrete indications" of attacks being planned in major cities Berlin, Hamburg and Munich.
Germany, which opposed the 2003 US-led invasion of Iraq but has nearly 5,000 troops in Afghanistan under Nato command, has never experienced an attack by militants on its own soil.
But authorities say the militant scene in Germany is large and dangerous.
The closest it has come to an attack was in July 2006 when militants placed suitcases with homemade bombs on two regional trains at Cologne's main station. They failed to detonate, averting an almost certain bloodbath.
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