Russell was one of five drivers punished for pit-lane speeding in the principality on June 7 and a failure by Mercedes to serve his penalty correctly meant he was also hit by a drive-through sanction which dropped him out of the points.
Championship leaders Mercedes served a 'right of review' when Alpine's Pierre Gasly had his Monaco podium reinstated after Formula One's governing body accepted there were inaccuracies over the pit-lane speeding measurements.
Gasly had been demoted from third to seventh after he was given two separate five-second time penalties.
McLaren, whose Australian driver Oscar Piastri had already served time penalties for the same offence earlier in the race, and Red Bull have lodged separate protests with the FIA Court of Appeal and they are ongoing, but Mercedes have opted not to pursue the matter.
"We can confirm we have withdrawn our Right of Review submission relating to the penalties received and served by George Russell during the Monaco Grand Prix," a Mercedes statement read.
"Following the decision to rescind Pierre Gasly's time penalty it was important for us to explore all available options to address the impact of George's pit-lane speeding penalty on his race result.
"We had a limited time window in which to apply for the right of review during the race weekend in Barcelona and did so in order to reserve our position in this regard.
"Our subsequent collaborative discussion with FIA and Formula 1 has shown their determination to review the unique circumstances arising from the Monaco Grand Prix and to proactively address the factors that caused them.
"In the face of this clear determination, we have concluded that further pursuit of our right of review application will not serve our team or the sport and thus we have withdrawn our submission."
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