Shur, who has been in the post for nine years, said that he was leaving as the company was entering into "new chapter" in the lead up to an initial public offering.
"It is a good time to hand over to a successor," he said.
Schur took on the role in 2005 in order to complete the merger of six energy companies — Elsam, Energi E2, Nesa, Kobenhavns Energi, Frederiksberg Forsyning and Dong.
At the same time, the company embarked on a move into green energy, which led to it becoming the global leader in offshore wind development.
Yesterday, the Danish parliament approved Goldman Sachs' investment in Dong despite loud objections from a large portion of the country's parliamentarians.
The DKK 8 billion (EUR 1.1 billion) investment in the company was given the nod by the Danish parliament's finance committee.
The banking giant will now hold a 19% stake in Dong. The deal also includes investment from Danish pension firms ATP and PFA to the sum of DKK 3 billion for a combined 7% stake.
Some in the wind industry have raised fears that such a buy-in from an investment bank could undermine the company's commitment to renewable energy and its move away from tradition energies such as oil.
Schur said: "Dong Energy has suffered financially from the fact that climate-damaging use of coal has been continued in so many European countries. But I still believe that Dong Energy should invest in being able to provide the green energy solutions of the future.
"Although, of course, in a well-considered and balanced way so that the company creates value for its owners."