Fridman is the second richest man in Russia, and is reported by Reuters to be one of the country's most influential tycoons.
In April the UK government threatened it would force him to sell his North Sea oil assets, over fears he or his company could be hit by new sanctions over the Russian occupation of Crimea.
Bildt has himself been hawkish on Russia, supporting sanctions and saying to American broadcaster REFL in March that Putin is "waiting to exploit weaknesses either in Ukraine or in the West."
As well as serving as conservative Moderate Party foreign minister of Sweden, Carl Bildt is also a former prime minister.
He has previously sat on the board of Swedish firm Lundin Oil, which Human Rights Watch has linked to abuses in Sudan in the 1990s, where people were forced off their land "to clear the way for foreign oil operations."