The Chancellor tells Britain there can be no "cherry picking" on the movement of goods, capital, people, and services.
Angela Merkel has warned the European Union must consider limiting the UK's access to the single market if it refuses to accept free movement.
The German Chancellor said Britain could not negotiate its future relationship with the bloc "based on a form of cherry picking".
Ms Merkel's remarks came after the Prime Minister told Sky News that Britain could not hold on to "bits of EU membership".
The pound fell to its lowest level against the dollar for two months in the wake of the comments, but Theresa May sought to play down their impact and said she was referring to the need for a new relationship with the EU.
She said: "People wanted us to take control of immigration and people coming to the UK from the EU.
"But we also want the best possible deal in trade with and operating within the single European market for British businesses and likewise for European businesses operating in and trading with the United Kingdom."
Ms Merkel told civil servants in Cologne that "cherry picking" by UK negotiators "would have fatal consequences" for the 27 states left in the EU.
"Britain is, for sure, an important partner with whom one would want to have good relations even after an exit from the EU," she said.
"(But) access to the single market is only possible under the condition of adherence to the four basic principles (movement of goods, capital, people, and services)."
Responding to Mrs Merkel's comments, the PM's official spokeswoman said: "We are about to enter a negotiation with 27 other countries.
"And as we prepare for those negotiations, countries will be talking about their positions and how they are going to approach them.
"The Prime Minister has been clear that the British people made clear it is important we take control of immigration but this shouldn't be a zero-sum game.
"And we should be approaching this on how we can get the maximum freedom for UK businesses to operate in and trade with the single market.
"There are many countries around the world that have free trade arrangements with the European Union."
SOURCE: Sky News
