Considering that around 1 million refugees and migrants entered Europe this year, yes, there is such precedent.
Between 1944 and 1950, following the offensive of Red Army, and Jalta, Teheran and Potsdam agreements, 13 to 16 millions ethnic Germans from Eastern and Central Europe had fled or been expelled to the Germany mainly from USSR, Poland, Czech Republic, Hungary, Yugoslavia and Romania. Another millions of people were relocated due to post-war geopolitical changes, i.e. 1,5 million Poles were deported from territories that used to be Poland and became USSR, to the territories that used to be Germany and became Poland etc.
It's really hard to give exact numbers here, considering what the situation was back then, but I think we can safely assume that about 20 million people permanently migrated from/to/within Central and Eastern Europe in the aftermath of WW2.
In terms of scale and rapidity of movement, the greatest forced mass migration in human history took place with the partition of India in 1947-48. An estimated 15 million people were forced to move between Pakistan and India in the year after they achieved independence, with somewhere between one and two million dying in the process.
Combined with the mass displacement of Europeans that /u/kostekbiernacki mentions (see this article for a discussion of the process), the period between 1944 and 1948 stands out as the greatest refugee crisis of the 20th century.
Collectively this crisis had a profound effect on the contours of the contemporary world. As Ayesha Jalal has written in the Pity of Partition,
Partition was both the central historical event in twentieth-century South Asia and a historical process that has continued unfolding to this day. It is common to hear in the subcontinent that the most pressing problems besetting India, Pakistan and Bangladesh today have their origin in the decisions of expediency taken in 1947.
Europe and the Middle East were also shaped by this movement of people - without the influx of Jewish "displaced persons", for example, Israel would probably not have had the critical mass of population necessary to achieve independence in 1948.
The outmigration of ancestral Puebloan populations from the Four Corners region of the USA in the 13th century was massive movement of people over a very short (roughly 30 year) period that had major social impacts on the Southwest.
You may be interested in this article written recently that frames this historical event in the Southwest in light of current events in Europe. While it is a pop piece, the author is a respected archaeologist and the underlying story is certainly the accepted archaeological narrative at the moment. A Refugee Story, A.D. 1275.