Mr Kempf warned the crumbling bloc’s freedom of movement as well as freedom of services, capital and the single market must not be “put into danger”.
The industry chief echoed Angela Merkel’s calls for a hard Brexit as she warned Britain would be be allowed to cherry-pick single market access.
“For politicians in Brussels and Berlin there should be only one motto — keep Europe together and make it stronger.
“The four basic freedoms of the EU are fundamental — there must be no borders for goods, services, capital and workers.”
But both Mr Kempf’s and Mrs Merkel’s recent comments signal Germany could try and force a hard Brexit.
The German Chancellor has repeatedly said free movement of EU citizens will remain a requirement for membership of the single market.
In a speech to members of the German Civil Service Association in the city of Cologne on Tuesday, she said: “One cannot lead these negotiations based in the form of cherry picking.
Angela Merkel warned Britain cannot cherry pick single market access
“Britain is, for sure, an important partner with whom one would want to have good relations even after an exit from the EU.”
She added “that on the other hand, we are clear that, for example, access to the single market is only possible under the condition of adherence to the four basic principles.
“Otherwise one has to negotiate limits of access.”
Mr Kempf said Brussels would not bow down to Britain’s demands for immigration contol
But the industry’s harder line comes as Theresa May admitted Britain will not be able to keep “bits” of its membership of the bloc.
The Prime Minister has repeatedly said she will not reveal her strategy before triggering Article 50 of the EU’s Lisbon Treaty in March.
Mr Kempf urged the Prime Minister not to delay the start of negotiations.
BDI sees growth of about 1.5 per cent this year for Germany
The BDI president also warned incoming president Donald Trump against attempts to seal off the US and limit free trade.
He said: “This would damage the whole global economy and in particular the export-oriented German economy.”
But despite Mr Kempf’s concerns, BDI sees growth of about 1.5 per cent this year for Europe’s biggest economy.
The German government has not released growth figures for 2016, but in October the BDI forecast that the economy would grow by 1.9 percent.
The BDI said it expected German exports to increase by 2-3 per cent in 2017 and the number of employed people to rise by up to half a million from last year’s level of 43.5 million.