"Neither side has an interest in putting up trade barriers," Weidmann, who also sits on the European Central Bank's Governing Council, said in a speech. "But the EU should also not give the UK a better treatment than it does to Switzerland and Norway."
He also said that while Brexit will weigh on euro zone growth and further dampen bank earnings, it is ultimately a political crisis so there is no need for more European Central Bank stimulus.
Britain's referendum sent markets into a tailspin, weighing on currencies and depressing bank shares, raising market expectation for more ECB stimulus to prop up growth.
"Monetary policy is already expansionary and I'm doubtful that an even more expansionary stance would have stimulatory effect at all," Weidmann said. "This is a political crisis which must be solved politically."
Weidmann said Britain was making a mistake by leaving the EU but that it was an opportunity for Frankfurt to become an even bigger financial hub. The German government should step up efforts to attract firms.
"For the Frankfurt financial center, new opportunities could arise," Weidmann said. "This will require political backing but we should welcome businesses relocating to Frankfurt from London.
The European Central Bank, Deutsche Bank, Commerzbank and the Bundesbank are all headquartered in Frankfurt, making the Germany city a key financial hub on the continent.
Though markets have calmed since the vote, Weidmann warned that heightened uncertainty is still possible, particularly for banks as the further decline in long term interest rates and the flattening of the yield curve will put already strained bank earnings under more pressure.
Calling the June 23 vote a watershed moment for Europe, Weidmann said Brussels had damaged the EU's reputation by consistently ignoring budget rules for big member states, eroding public confidence in the institution.
He also warned against expanding risk sharing, such as in the proposed common deposit insurance scheme, since the euro zone's current fiscal framework does not enforce responsibility, placing an undue burden on countries with sound finances.