Baerbock, on a visit to Beirut, said the military aid was aimed at helping the Lebanese army better secure the southern border with Israel.
The army must be able to exercise "effective control" over the area in order to "contain armed militias and terrorist organisations", she said.
Lebanon's Iran-backed militant group Hezbollah and its arch-foe Israel have been exchanging near-daily fire across the border since the Israel-Hamas war broke out on October 7. Hezbollah is a Hamas ally.
The cross-border unrest has sparked fears of a wider regional conflict, prompting a succession of Western diplomats to converge on Beirut to urge restraint and discuss political solutions.
Baerbock, who held talks with Lebanese Prime Minister Najib Mikati, said an escalation of the conflict "would be a catastrophe for the two countries".
She called on Hezbollah to withdraw from the border region with Israel, as required under United Nations Resolution 1701.
Resolution 1701, which ended a 2006 war between Israel and Hezbollah, called for the removal of armed personnel south of Lebanon's Litani River, except for United Nations peacekeepers and Lebanese state forces.
"The war in Gaza against Hamas must not be used as an excuse to open another front and provoke a regional war," Baerbock said.
Baerbock made the comments during a visit to the German frigate "Baden-Wuerttemberg" at the port of Beirut.
German soldiers are part of the UNIFIL peacekeeping force tasked with monitoring the area on the Israeli-Lebanese border.
The 15 million euros pledged by Germany will go towards procuring fuel as well as medium-term measures such as border surveillance training for Lebanese troops, Baerbock said.
The October 7 Hamas attack on Israel resulted in about 1,140 deaths in Israel, mostly civilians, according to an AFP tally based on official figures.
Israel has responded with a relentless military campaign that has killed at least 23,357 people, mostly women and children, according to the Gaza health ministry.
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