The meeting, at Mr Putin's summer residence in Sochi, comes at a low point in bilateral relations over the war in Syria and Russia's annexation of Crimea.
They are expected to discuss both issues during their meeting - but no breakthroughs are expected.
Mr Putin will then meet Turkish leader Recep Tayyip Erdogan on Wednesday.
Ties between Russia and Germany have worsened since Russia's 2014 annexation of Crimea in Ukraine, with Germany being a driving force behind the EU sanctions imposed in response.
The pair, who are among the most powerful world leaders, have crossed paths at international summits recently.
But this meeting - with the official purpose of discussing the G20 summit of world leaders to be held in Hamburg in July - is the first trip Mrs Merkel has made to Russia in two years.
Mrs Merkel wants Russia to seek an end to the conflict in Ukraine by using its influence on pro-Russian separatists, and also needs Moscow's co-operation to bring peace to Syria, the BBC correspondent in Berlin, Damien McGuinness, says.
But President Putin equally needs Mrs Merkel's support in to lift the EU's sanctions, our correspondent adds. Mr Putin is also keen to hear her opinion of US President Donald Trump, whom she recently met.
The pair spoke frequently before the breakdown in communications since 2014, and were said to have a grudging respect for one another.
She speaks Russian, having grown up in communist East Germany, and he speaks German, from his years working for the KGB in Dresden in the 1980s.
Russian news outlet Tass said the pair would discuss terrorism, the Middle East, and the Minsk agreements on the Ukraine crisis, quoting a Kremlin press source.
But both sides have downplayed the prospect of major breakthroughs during their meeting in Sochi.
Germany remains critical of Russia's actions in Crimea in 2014, and the two leaders stand opposed on the war in Syria.
The German domestic intelligence agency has also accused Russia of being behind a series of cyber attacks on state computer systems.
In contrast, Mr Putin's scheduled meeting with the Turkish president the following day comes at a time of increased co-operation between the two nations.
While they back opposing sides in Syria's civil war - with Moscow supporting Syrian President Bashar al-Assad, and Ankara his opponents - the two countries began carrying out joint air strikes against the so-called Islamic State in January.
The joint operation came a little over a year after Turkey shot down a Russian military jet, resulting in a crisis in bilateral relations.
US President Donald Trump is also scheduled to speak to President Putin by phone on Tuesday, the White House announced Monday night. They are expected to discuss the war in Syria.
German Chancellor Angela Merkel is due to meet Vladimir Putin in Russia for the first time since 2015.