Hubertus Andrae told a news conference that German officials had received a "very concrete" tip that suicide attacks were planned on New Year's Eve at two train stations.
Police closed the central and Pasing stations about an hour before midnight, and reopened them hours later.
"We received names. We can't say if they are in Munich or in fact in Germany," Andrae said.
"At this point we don't know if these names are correct, if these people even exist, or where they might be. If we knew this we would be a clear step further. We have no information that these people are in Munich or in Germany," he added.
The alarm came as Europe entered the New Year under a state of heightened alert, seven weeks after Islamist militants killed 130 people in shootings and suicide blasts across Paris.
Bavarian Interior Minister Joachim Herrmann said the Munich tip, which media reports said came from French intelligence, indicated that the Islamic State militant group was behind the planned operation.
Herrmann told reporters later on Friday that the police presence at the train stations had been reduced.
"We all know that there is a high risk of attacks in Europe and also here in Germany and Bavaria. But we don't have a concrete indication that there will be an attack today or tomorrow at a specific location," he said.
Thomas de Maiziere, interior minister in the federal government of Chancellor Angela Merkel, said: "The situation in Europe and also in Germany remains serious in the New Year. Security forces anticipate the high threat of international terrorism to persist."
Police said they had received information that five to seven suicide bombers were planning to take part in the attack.
Previous warnings
After the deadliest year for militant attacks in Europe since 2004, the build-up to the New Year had been overshadowed by arrests, security warnings, and the scaling-back of big traditional celebrations in Brussels, Moscow and Paris.
On Dec. 26, police in the Austrian capital Vienna said a "friendly" intelligence service had warned European capitals of the possibility of a shooting or bomb attack before New Year. That tip, too, had included the names of several suspects.
In Belgium, authorities on Wednesday called off the usual New Year's Eve fireworks display in the capital, citing fears of a possible militant attack. Police said on Thursday they were holding three people for questioning over an alleged plot.
Throughout the Munich alert, police kept up a stream of messages in several languages on Twitter, at times alternating incongruously between security warnings and New Year greetings.
"Good morning to those, who spent the night out in #munich! Thanks for staying calm and for your understanding concerning our measures," the latest message in English said.
The episode highlighted the dilemma facing authorities across the continent as they try to communicate potential threats without causing undue panic or disruption.
Herrmann, the Bavarian minister, urged the public to resist "being driven crazy by terrorists as we enter a new year in 2016. We need to take the danger seriously, but we can't let them change the way we live here in Germany."
