Germany's Defence Ministry has confirmed newspaper reports that the incident took place, without saying when or why it happened.
According to the report in the Tagesspiegel newpaper, two Israeli F-16 planes fired shots as well as anti-missile defence flares while flying low over the German vessel.
The newspaper said the incident had been reported to parliament on Wednesday by a state secretary in the defence ministry,
Christian Schmidt.
A spokesman for the command of the German mission in Lebanon said it was investigating Monday's incident.
Israeli denial
Israeli Defence Minister Amir Peretz denied his country's planes had opened fire on the German ship, in a telephone call with German counterpart Franz Josef Jung.
"No Israeli plane opened fire at a German ship and Israel has no intention of attacking the German forces," Mr Peretz said, according to his spokesman.
France and the United Nations this week warned Israel that it was endangering the multinational peace mission in Lebanon by sending its fighter planes into Lebanese airspace.
Police in Lebanon have claimed that there were more Israeli flights over their country on Monday than on any other day since the end of the Jewish state's 34-day war with Hizbollah.
Last weekend Mr Peretz said the flights through Lebanese airspace would continue because of alleged arms smuggling to the militant group Hizbollah since the end of the war on August 14.
Uneasy peacekeepers
Germany is heading the naval component of the UN peacekeeping force in Lebanon but has refused to contribute ground troops in a bid to avoid clashes with Israeli forces because of lingering sensitivities over the Holocaust.
The German press also reported that the German navy has been told that their mandate does not allow them to come within 10 kilometres of the Lebanese coast unless asked to do so by Beirut.
The issue had been the subject of protracted wrangling between
Beirut and Berlin before eight German vessels set sail for Lebanon on September 21 with some 1,000 soldiers on board.
The German government said at the time that it had won assurances that its ships would be allowed to search Lebanese waters and to use force if necessary to intercept weapons being smuggled to Hizbollah.
The UN mandate also stipulates that German soldiers may only set foot on suspect ships or seize material if they are accompanied by Lebanese forces.