The Mercedes driver faced investigation after sliding down the escape road at Turn 5 (Mirabeau) during his final flying lap, bringing out yellow flags that prevented those behind - including team mate Lewis Hamilton - from improving.
Rosberg held provisional pole at the time of the incident, with his first run having produced a lap just five-hundredths of a second faster than Hamilton's.
Rosberg subsequently apologised for his mistake, while Hamilton insisted he had been "on target" to beat the German to pole before being forced to abandon his lap.
"The stewards examined video and telemetry data from the team and FIA and could find no evidence of any offence related to the turn 5 incident," read a statement from the stewards.