"Travel to Israel and East Jerusalem is urgently discouraged," the ministry said in an advisory on its website.
The advice had previously applied only to certain parts of Israel but now takes in the whole country, a ministry source confirmed.
Earlier, the United States authorised the departure of non-emergency embassy staff from Israel as it threatened strikes on Iran and pressed its biggest military build-up in the Middle East in decades.
The move came a day after latest Oman-mediated talks between Iran and the United States seen as a last-ditch bid to avert war. Initial optimism was tempered by Tehran warning Washington must drop "excessive demands" to reach a deal.
Britain also said it had moved some of diplomatic staff and their dependants from Tel Aviv to another location in the country.
The German foreign ministry source told AFP its embassy in Tel Aviv remained "fully operational".
"We are monitoring the situation very closely and are in close contact with our embassy in Tel Aviv, including regarding the security situation of our colleagues on the ground and their families," the source said.
Germany is "in close contact with our embassy in Tehran, including regarding the security situation of our colleagues on the ground", the source added.
However, due to diplomatic tensions with Iran, "our embassy in Tehran has not been fully staffed for some time" and is "only able to provide very limited consular assistance on the ground", the source said.
Lufthansa announced Saturday it has cancelled it flights to and from Tel Aviv, Beirut, Amman, Erbil and Tehran until March 7, as the US and Israel launched air strikes on Iran, which retaliated with missile launches.
The German airline group said in a statement it and its subsidiaries were also suspending flights to and from Dubai and Abu Dhabi until Sunday. It said the cancellations were due to the "current situation in the Middle East".
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