German Foreign Minister Frank-Walter Steinmeier said negotiations should begin as “soon as possible”.
He made the comments after an urgent meeting of the six EU founder members to discuss the decision.
British PM David Cameron has said he will step down by October to allow his successor to conduct talks.
The six countries attending the talks in Berlin – Germany, France, Italy, Belgium, Luxembourg and the Netherlands – first joined forces in the 1950s and still form the core of the EU.
Mr Steinmeier said quick negotiations were essential so members could “focus on Europe’s future”.
EU ‘taken hostage’
The first summit of EU leaders with no British representation will be held on Wednesday, a day after Mr Cameron holds talks with members.
Global stock markets fell heavily on the news of the so-called “Brexit”, where the UK voted by 52% to 48% to leave the EU. The value of the pound has also fallen dramatically.
Credit rating agency Moody’s dcut the UK’s outlook to “negative” after the poll.
The UK must now invoke Article 50 of the EU Lisbon Treaty, which then allows for two years for withdrawal to be negotiated.
European Commission head Jean-Claude Juncker said the EU-UK split was “not an amicable divorce”, but nor had they had a “deep love affair”. He said exit negotiations should begin immediately.
“Britons decided yesterday [Thursday] that they want to leave the European Union, so it doesn’t make any sense to wait until October to try to negotiate the terms of their departure,” Mr Juncker said in an interview with Germany’s ARD television network.
In another interview, with Bild newspaper, he said it was “first and foremost” a matter for Britain’s EU commissioner Lord Jonathan Hill to decide whether to stay in his role, in charge of EU financial services.
Also on Friday, European Parliament President Martin Schulz said the EU “as a whole was taken as a hostage” by infighting among Mr Cameron’s Conservative party.
“OUTsch!,” “Well done little Britain,” “Completely detached.”
Germany’s press reflects the widespread shock at the British decision to leave the EU. At the highest level of government no-one really expected this. And they are scrambling to defend German and European interests.
The German position is focused on two major, and delicate, decisions.
Firstly, whether to use Brexit as an opportunity to deepen European integration, or to view it as a “wake-up call” and create more flexibility within the union.
And, secondly, how to deal with Britain – an important trading partner – as a ‘third country.’
Senior economists and business leaders warn against barriers to free trade.
But politicians are talking tough. Concessions, they say, might encourage other member states to leave. For this reason one senior MP told me “there must be consequences for Britain”.\