Speaking at a press conference alongside May ahead of the working dinner between two of the world's most powerful women, Merkel said that Britain and Germany had friendly relations and shared values.
Bilateral relationships and trade between them would continue after Britain's departure from the European Union, she said.
But Merkel said that while the general issue of the impending Brexit would be broached, neither formal nor informal negotiations on the subject could begin until Article 50 of the Lisbon Treaty -- which officially kicks off the exit process and opens a two-year window for exit negotiations -- was triggered.
Speaking after Merkel, May said that both sides wanted to maintain "the closest possible economic relations between our two countries, and I believe that is what German and British business want too."
She said the business of negotiating Britain's exit from the bloc would take time and "require serious and detailed work."
"I want to work with Chancellor Merkel and my colleagues around the European Council in a constructive spirit to make this a sensible and orderly departure," she said.
"All of us will need time to prepare for these negotiations and the United Kingdom will not invoke Article 50 until our objectives are clear. And that's why I've said already, this will not happen before the end of this year."
She said that she understood that the delayed triggering of the article "will not please everyone."
"But I think it is important to provide clarity on that now."
May will follow her Berlin trip with a visit to Paris for talks Thursday with French President Francois Hollande, where she is expected to convey a similar message about Article 50, according to a statement from 10 Downing Street.
Tensions over when EU exit begins
Following the June 23 vote to leave the EU, Britain now faces a complicated process of negotiations to remove itself from the bloc.
EU leaders have uniformly said they will not enter into formal exit negotiations with Britain until it triggers Article 50, and have urged Britain to move swiftly.
But the British government does not plan to trigger Article 50 before the end of the year
, the country's High Court heard this week.
Officials will need time to consult with the governments of Scotland, Wales and Northern Ireland, as well as with various industry sectors, to work out the UK's objectives for the negotiations, according to a statement from 10 Downing Street.
Both Scotland and Northern Ireland, constituent countries within the United Kingdom, voted in the referendum to remain in the EU, and the vote to leave has revived talk in both countries of leaving the UK instead.
The trips to Paris and Berlin were intended to build May's relationships with key European leaders ahead of the critical Brexit negotiations.
"These visits will be an opportunity to forge a strong working relationship that we can build upon and which I hope to develop with more leaders across the European Union in the weeks and months ahead," May said in a statement Wednesday.
May also told European Council President Donald Tusk on Tuesday that Britain would not take up its scheduled presidency of the council in 2017. The presidency of the European Council is rotated between member states.
First questions in Parliament
The Berlin meeting was the second major test of May's premiership Wednesday, a week after she succeeded David Cameron, who stepped down as PM after his unsuccessful campaign to persuade Britons to remain in the EU.
Earlier in the day, May made her debut at Prime Minister's Questions in Parliament, fielding questions from lawmakers. During the session, she reiterated her commitment to Britain leaving the EU, following the vote to do so in a referendum last month.
But although the country is leaving the EU, May said, "The United Kingdom is not leaving Europe."
"I'm very clear, Brexit does mean Brexit," she said.
"We will make a success of it. What we need to do in negotiating the deal is ensure that we listen to what people have said about the need for controls on free movement. But we also negotiate the right deal, and the best deal for the trade of goods and services for the British people."
She also stressed that Britain should not be limited by focusing exclusively on its relationship with its European neighbors but should instead look to build ties throughout the world.
The session, a key test of her parliamentary authority amid hostile questioning, opened with fiery exchanges between May and Jeremy Corbyn, leader of the opposition Labour Party.
In response to Corbyn's questions, May said that while Labour, embroiled in a leadership crisis, might spend the next few months tearing itself apart, "the Conservative Party will spend those months putting the country back together."
She took another shot at Corbyn's shaky leadership after he attempted to raise the issue of workers' rights.
"I suspect there are many members on the opposition benches who might be familiar with an unscrupulous boss, a boss who doesn't listen to his workers, a boss who requires some of his workers to double their workload and ... maybe even a boss who exploits the rules to further his own career," she said pointedly.
"Remind him of anybody?"