Visoiu and King were both handed five-place penalties for the feature race at Sochi.
Rapax driver Visoiu made contact with Alexander Rossi at the Roggia chicane.
The incident sent both drivers into a spin, and forced them to retire, damaging Rossi's remaining hopes of catching Stoffel Vandoorne in the championship.
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Rossi's Racing Engineering team-mate King made contact with Norman Nato going into the race's first corner.
King lost his front wing and damaged his suspension, while Nato went on to retire in a cloud of smoke straight afterwards.
Artem Markelov was given a five-second penalty for contact with Julian Leal at the Roggia chicane.
Markelov left the track at the chicane but collided with the helpless Leal when he rejoined.
The penalty drops the Russian Time driver down five places to 14th.
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