The German chancellor said she believed Britain would stick to the timetable, adding the European Union was "ready".
Mrs Merkel added she hoped Britain would remain a good partner following the talks, due to begin on 19 June.
It is her first comment since Mrs May's Conservative party lost 13 seats.
The loss left the Conservatives eight MPs short of a majority in parliament, plunging negotiations into uncertainty. Mrs May called the snap election in order to secure a clear mandate for her vision of Brexit.
A spokesman for Mrs Merkel had previously refused to be drawn on the issue out of "politeness and respect" while the process of forming a new UK government was under way.
Mrs May says she will form a government with the Democratic Unionist Party from Northern Ireland, which won 10 seats.
British PM Theresa May called an election to strengthen her mandate
Mrs Merkel, who is meeting with Mexican President Enrique Pena Nieto to discuss trade, told reporters gathered in Mexico City on Friday: "I assume that Britain, from what I heard from the prime minister today, wants to stick to its negotiating plan.
"We want to negotiate quickly, we want to stick to the time plan, and so at this point I don't think there is anything to suggest these negotiations cannot start as was agreed."
Mrs Merkel went on to say she hoped the UK would remain a good partner.
"Britain is part of Europe, even if it will no longer be part of the European Union."
However, she added the EU countries would be "asserting the interests of the 27 member states that will make up the European Union in future" during negotiations.
Mrs May failed to get the majority she had sought
Meanwhile, Michael Fuchs, senior economic adviser to the German chancellor, told meant it was time for Mrs May "to face realities" and soften her approach.
"Her wish and will was not really too much accepted by the British people," he said. "I have the feeling, because otherwise they would have given her a better vote.
"Maybe, this is a chance that we can come up to a more reasonable Brexit negotiations because in the last time (recently) I really had the feeling that everything was just being very tough and it doesn't make sense to be tough.
"We want to have a fair deal with Britain and we want to have a fair final Brexit negotiations."
Other EU leaders have expressed concerns the failure to win a majority may make negotiations even more difficult.
Brexit negotiator Guy Verhofstadt, who is president of the Alliance of Liberals & Democrats for Europe in the European Parliament, had caustic words for Mrs May.
"Yet another own goal, after Cameron now May, will make already complex negotiations even more complicated," he tweeted.
Jean-Claude Juncker, head of the European Commission, said he wanted discussions to proceed without delay, while Michel Barnier, the EU's chief negotiator for Brexit, said "negotiations should start when UK is ready".
European Council President Donald Tusk alluded to the March 2019 deadline for Brexit talks.
"We don't know when Brexit talks start. We know when they must end. Do your best to avoid a 'no deal' as result of 'no negotiations'," he wrote.