Speaking to the BBC on Wednesday, Herman Van Rompuy described the UK's decision to leave the EU as a "political amputation".
He said negotiations were unlikely until a new German government was formed.
"Before the German elections and before there is a new German government, I think no serious negotiations will take place," he told BBC Radio Four's Today programme.
"You can always start with more technical matters, but the hardcore, the difficult topics, will be tackled after the constitution of a new German government and that will be October/November."
British Prime Minister Theresa May has previously said that she will not trigger Article 50 - the formal start of the process of leaving the EU - before 2017.
Leaders of the 27 EU countries will begin to gather on Thursday in the Slovakian capital of Bratislava to discuss the future of the bloc.
Van Rompuy denied leaders wanted to "punish" the UK for leaving the EU, but said there was a desire not to encourage other countries to leave.
"Any negotiation will be a difficult negotiation, independent of the personalities. Of course we want an agreement which represents some kind of mutual benefit," he added.
The UK voted to leave the EU in a referendum on June 23.