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.
Former Japanese Prime Minister Taro Aso, a senior figure in the country's ruling party, met with Donald Trump on Tuesday, becoming the latest US ally seeking to establish ties with the Republican presidential candidate.
Russian missiles damaged residential buildings and injured six people in Ukraine's second-largest city, Kharkiv, early on Wednesday, Governor Oleh Synehubov said on Telegram.
Five migrants died in an attempt to cross the English Channel from France to Britain in an overcrowded small boat on Tuesday, hours after Britain passed a bill to deport asylum seekers to Rwanda in a move to deter the dangerous journeys.
Israel bombarded northern Gaza overnight in some of the heaviest shelling in weeks, causing panic amongst residents and flattening neighbourhoods in an area from which the Israeli army had previously down its troops, residents said on Tuesday.
Russia launched a drone attack on Ukraine that injured seven people in the Black Sea port of Odesa, two of them children, and also targeted Kyiv, the capital, Ukraine's military officials said early on Tuesday.