The first of the ships, the frigate Karlsruhe, pulled away from the dock at the North Sea port at Wilhelmshaven and moved smoothly across the calm harbor after a farewell ceremony.
The German force of two frigates, two support vessels and four fast patrol boats, along with three ships from Denmark, are to arrive off the Lebanese coast in 10 to 14 days.
"Unless the weapons are silent there is no chance for peace in the Middle East," Jung said at the ceremony.
Germany is taking charge of a multinational naval task force with a mandate to prevent arms shipments from reaching Hezbollah — a key component of the cease-fire agreement.
The naval detachment is led by the 459-foot frigate Mecklenburg-Vorpommern, equipped with a 76 mm cannon and space for two patrol helicopters.
Parliament approved the deployment on Wednesday, although some lawmakers voted against it because of misgivings linked to Germany's Nazi past and the Holocaust.
Chancellor Angela Merkel ruled out sending combat troops to Lebanon in an attempt to ensure that no German soldiers could get caught up in any confrontation with Israeli forces.
Parliament approved a mandate allowing the deployment of up to 2,400 service personnel. Germany is also sending police and customs officers to advise and train Lebanese security forces on tightening border controls.