The demand has been made by three organisations: Friends of the Earth Europe, LobbyControl and Corporate Europe Observatory.
They have written to Parliament President Martin Schulz expressing "concern" about a potential conflict of interest case concerning Niebler and asked the Commission to launch an investigation.
Niebler, an MEP with the EPP group since 1999, is said to have combined her work as a deputy with her career as a lawyer with various law firms.
According to the three groups, the deputy "has worked in law firms that were (at least part of the time) not registered in the EU transparency register and that are involved in lobbying activities at the EU level."
The letter, seen by this website, states, "It is our opinion that Niebler's additional paid work in the legal sector places her in a position of a potential conflict of interest and also represents a lack of due respect for Parliament's reputation."
Responding to the allegations contained in the letter, Niebler told this website, "There is no conflict of interest. I strictly differentiate between my parliamentary work as MEP and my work as a lawyer.
"I have been practicing law now for more than 25 years, long before I became an MEP. It goes without saying that you will find my activity as a lawyer listed in my 'declaration of my financial interests' as published on the official website of the EP as well as on my website.
"Let me stress that there is a big difference between practicing law, i.e. advising on legal issues, and representing clients' interest, i.e. lobbying. I have never worked as a lobbyist."
It is claimed that in her declaration of financial interests, submitted in July 2014, she registered her activity as 'of counsel' for the IT and media department of the law firm Bird & Bird (with a monthly salary of €1000 to €5000).
The three groups said, "Bird & Bird is currently not registered in the EU's transparency register. The firm had been registered until 28 April 2015, when the register's secretariat removed its entry due to the failure to update it."
They go on, "Neibler left Bird & Bird in the summer of 2015 to join Gibson, Dunn & Crutcher. In her declaration of financial interests submitted on 31 August 2015 and updated on 20 January 2016 she declared a monthly income of €1000 to €5000 from her work 'as counsel' for the law firm."
In a press release, Michael Walther, a partner leading the law firm's Munich office, was quoted as saying that, "Angelika has a profound legal background and knowledge of the European dimension of intellectual property and data privacy questions that matter to our clients, and we are looking forward to benefit exceptionally from her expertise, insights and experience."
In the letter to Schulz, the NGOs say, "We call on you to investigate in order to clarify the situation of this MEP and whether she is acting in full compliance with the provisions of the code of conduct."
The letter continues, "Ms Niebler should be asked to clarify the nature of her activities as a lawyer, the names and interests of her clients, and what overlap exists between their interests and her work as an MEP."
Parliament is also asked to investigate if the deputy observed the principle of showing "respect for Parliament's reputation" by "undertaking paid work for an organisation which appears to engage in EU lobbying while not being part of the EU transparency register."
The letter adds, "It harms the Parliament if its own members are even not taking the transparency register seriously."
It wants the institution to ensure that all MEPs' declarations of interests are updated so that they "properly reflect the nature and the details of their outside activities and interests."
The campaigners also call on Parliament to "remain firm in its resolve to support a legally-binding lobby transparency register so that all EU lobbyists are forced to declare their lobby spending, the issue they lobby on, and the full list of lobby clients."
Myriam Douo, transparency and better regulation campaigner for Friends of the Earth Europe, said, "We recognise that the code of conduct does not prevent MEPs from having a second job.
"But when MEPs put themselves in the situation of having a second job with companies which lobby the EU and where the MEP works on issues which are relevant to the second employer, it creates a conflict of interest risk, between the interests of the employer on the one hand, and the public interest as represented by MEPs on the other hand.
"This is why we firmly believe that the code of conduct needs amending to prevent MEPs from having additional paid work with organisations that lobby the EU, in order to prevent conflicts of interest."