In a letter, the members say they want a full examination of public interest concerns about media plurality and broadcast standards.
The letter is signed by S&D group deputies Brando Benifei, Neena Gill, Catherine Stihler and Julie Ward.
It has been sent to Karen Bradley, UK Secretary of State for culture, media and sport; Matthew Hancock, Minister of State for digital and culture in the UK; Sharon White, Ofcom Chief Executive and Margrethe Vestager, European competition Commissioner.
The UK government says it is seeking a review of the merger by Ofcom and the Competition and Markets Authority.
The Media Reform Coalition in the UK has issued a report on what it calls the "expected negative impact" on news plurality in the UK resulting from the proposed Fox/Sky plc merger.
The four MEPs say the report notes a merger would "result in the merged entity being the only news and media provider present on all four media platforms at the wholesale level, with a significant presence across them.
"In particular, the merged entity will effectively become: the largest newspaper provider; the third largest TV news provider; the second largest provider of radio news content; the fourth largest online news provider."
The MEPs' letter says, "The report raises serious questions about news plurality in the UK that warrant a more detailed review of the proposed transaction.
"Additionally, the proposed transaction also poses similar questions regarding the broadcasting of sport in Europe, taking into account Sky's position of dominance.
"Therefore, we would like to ask the UK government and Ofcom to consider the consequences of allowing these two powerful companies to merge and the dangers of increasing horizontal concentration in news media in UK and consequentially in Europe."
It goes on, "We would like to ask the UK government and Ofcom to take the necessary time to conduct a detailed review of the media plurality and broadcasting standard concerns raised by the Media Reform Coalition. Failure to do so would risk long-term damage to the diversity and quality of the media in the UK. An independent and competitive news industry is vital to any democracy."
The letter adds, "The government should not allow one corporation to gain such significant control of media in the UK, without an exhaustive review."
On Thursday, Neena Gill explained the reasons for raising the issue, telling this website, "Our democracy depends on a diverse news industry holding it to account. The proposed merger between Fox and Sky PLC jeopardises this diversity by giving too much control to one corporation and one man: Rupert Murdoch."
She added, "In recent times we have seen all parts of the media become more partisan. This should highlight the dangers of one man having dominance over our newspapers, television, radio and online news."