Since the start of the war on Feb. 24 until May 11, 727,205 people have registered in Germany's Central Register of Foreigners (AZR), of which 93% hold Ukrainian citizenship.
Welt am Sonntag newspaper reported on Saturday, citing Interior Ministry data.
A significant number may have travelled on to other European Union countries or returned to Ukraine, it said.
Around 40 per cent of Ukrainian refugees were minors, and women make up 81 per cent of the adult refugees registered, Welt added.
The Russian invasion has triggered a massive displacement of people, including more than eight million Ukrainians within the country, according to the latest International Organization for Migration (IOM) report.
The number of people who have fled Ukraine has passed six million, in Europe's worst refugee crisis since the end of World War Two, a UN refugee agency said on Thursday.
President Donald Trump said talks with Iran to end the war could soon resume and end in a deal, telling the world to watch out for an "amazing two days", while US forces imposing a blockade turned back vessels leaving Iranian ports.
At least 17 people died and 36 others were injured following a suspected boiler explosion at a power plant operated by India's Vedanta Ltd in the central Indian state of Chhattisgarh, a government official said on Wednesday.
US Secretary of State Marco Rubio hosted a rare meeting between Israeli and Lebanese envoys in Washington on Tuesday, saying he hoped the two countries would agree to a framework for a peace process, even as Israel pressed its war on Hezbollah.
Negotiating teams from the US and Iran could return to Islamabad this week to resume talks to end the war, sources told Reuters on Tuesday, after the collapse of weekend negotiations prompted Washington to impose a blockade on Iranian ports.
Around 250 people were missing after a boat carrying Rohingya refugees and Bangladeshi nationals capsized in the Andaman Sea, the United Nations' refugee and migration agencies said in a joint statement on Tuesday.