Of the million, around 400 chose to head north to Belarus.
More than 1.3 million Ukrainians have fled their homeland in just over a week, the latest figures from the UN Refugee Agency (UNHCR) reveal.
In the 10 days since Russia's invasion, 1.37 million people have left Ukraine.
Of those that left between 24 February and 4 March, more than half went to Poland. Hungary and Moldova were the second most popular choices.
A further 133,000 Ukrainians sought refuge in "other European countries". The UNHCR did not specify which ones.
More than 53,000 have meanwhile crossed the border into Russia. These come on top of the 96,000 people who evacuated separatist-held areas in eastern Ukraine in the days leading to the assault. A further 406 headed for Belarus.