South East Labour MEP Anneliese Dodds called for an investigation in an amendment to the European Parliament's annual competition report earlier this month, which passed by 467 votes to 156, with 86 abstentions.
Margrethe Vestager, the European Commissioner for Competition, has written to Dodds to say the matter will not be taken any further.
Vestager said: "The transaction was notified to national competition authorities in several member states, namely Austria, Spain, Portugal and the United Kingdom, all which approved it last year."
Dodds says smaller teams are "unfairly punished" because of the way F1 is run.
As well as the sport's takeover by Liberty Media, Dodds also expressed concerns over its UK tax arrangements.
Dodds pointed to the recent collapse of the Manor team as an example of how the sport is failing some teams.
"Smaller teams are unfairly punished by an uncompetitive allocation of prize money that will always give the biggest teams more money, even if they finish last in every race," she said.
In 2015, two of F1's smaller teams, Force India and Sauber, asked the EU's Competition Commission to investigate the sport due to perceived unfairness over the way revenues were divided and rules decided.
The Commission has not yet ruled out an investigation into this issue.
The European Commission has rejected a call from hundreds of Euro MPs to investigate the takeover of Formula 1 by Liberty Media.