The answer is, yes!

Human capital flight is a well known economic phenomenon. Historically, it has occurred by both coercion, such as when the Jews were expelled from Spain or the expulsion of Germans from Eastern Europe. It also was something caused by governmental policies, as the Eastern Bloc in the Cold War sought to prevent an inevitable mass defection, which did indeed occur in East Germany before restrictions were completely closed. By the time this occurred, 1 in 5 East Germans had left for West Germany.

Iran had an exodus of it's intellectuals and "brains" after the Iranian Revolution, similar to the Huguenout exodus from France. Starting in the 1960s after decolonization, Africa began to lose a large proportion of its educated professionals due to the conflict and poverty. According to the United Nations Development Programme, Ethiopia lost 75% of its skilled workforce between 1980 and 1991. that is an incredible drain on any economy.

It is after 1994 so it can't be cited as historical, but it is worth mentioning contemporary examples such as India, which estimates that Indian students going abroad for their higher studies cost India a foreign exchange outflow of $10 billion annually.

Sources:

Court of the Red Tsar, by Simon Sebag-Montifiore

Jewish History Sourcebook, Fordham University

Berlin 1961, by Fredrick Kempe

And links in the comments.

Did American cities encounter any problems during the "White Flight" in the 1950s?