Unease about Britain's EU farewell sent the mood among German investors plunging in July to its lowest since November 2012, according to the first major sentiment snapshot of the post-Brexit era in Europe's largest economy.

The Mannheim-based ZEW institute says its economic sentiment index sank to -6.8 points in July, from 19.2 in June. That reading compares with a Reuters consensus of 9.0 and is lower than any of the economists polled had predicted.

"Uncertainty about the vote's consequences for the German economy is largely responsible for the substantial decline in economic sentiment," ZEW president Achim Wambach said.

The plunge in morale to a level not seen since the eurozone was in the throes of economic crisis prompted concern that German growth could weaken at a time when the traditionally export-oriented economy is already having to increasingly rely on domestic demand.

Worries about the stability of the banking and financial system following the 'Leave' vote in the June 23 referendum in Europe's main financial centre could also take their toll on Germany, Wambach said.

The ZEW index was based on a survey of 220 analysts and investors conducted from July 4 to 18, giving participants time to make an initial assessment of the impact Brexit could have.

Britain is Germany's fifth-biggest trading partner for goods and the German chamber of commerce has cut its forecasts for exports there, while the VDMA engineering association expects Brexit uncertainty to reduce demand for German goods.

The ZEW separate gauge of current conditions fell to 49.8 points from 54.5 in June - also below the Reuters consensus forecast for a reading of 51.8.

A broader take on fallout from Brexit will emerge on Wednesday, when eurozone consumer confidence data is due. Economists polled by Reuters have forecast a decline.

Florian Hense, economist at Berenberg in London, said that while post-Brexit market movements had been "relatively orderly" so far, the weak ZEW survey would worry policymakers at the European Central Bank.

President Mario Draghi would probably "take a dovish tone" at the bank's news conference after its rate-setting meeting on Thursday, Hense said.

But he also cautioned that sentiment data could "overreact to uncertainty more than hard economic data", and the eurozone economy should emerge relatively unscathed "as long as the contagion risk is contained".

Thomas Gitzel, economist at VP Bank, agreed that Tuesday's headline ZEW reading might be disproportionate.

It was yet to be seen whether the German economy would be hit hard by Brexit this year and the indicator could rise again in August.

"It's conceivable that the German economy will get off lightly," he said.

The Economy Ministry in Berlin has expressed concern about increasing economic risks for Germany in view of Brexit but has declared Europe's economic powerhouse is still in good shape while the Bundesbank has said for now it only sees a limited near-term impact.

A survey by Frankfurt-based Sentix had already shown sentiment and expectations in Germany falling in July.