A statement from Nextcloud said the complaint had been made to the European Commission and Germany's competition authority, with a complaint in France anticipated.
The 31 companies, which have banded together under the name Coalition for a level playing field, accused Microsoft of integrating its 365 service deeper and deeper in its software.
"OneDrive is pushed wherever users deal with file storage and Teams is a default part of Windows 11," the statement said.
"Behaviour like this is at the core of this growth of the tech giants and has to be stopped.
"This is a similar situation to the late 1990s when Microsoft bundled Internet Explorer with Windows to compete with Netscape. This is not an incident. Other big tech firms like Google and Amazon are doing a similar thing and the EU should take a stand."
The coalition has asked the EU to ensure:
No gate keeping (by bundling, pre-installing or pushing Microsoft services) for a level playing field.
Open standards and interoperability that make an easy migration possible. This gives consumers a free choice.
The statement said Nextcloud had filed an official complaint with the EU Directorate-General for Competition about Microsoft's behavior of Microsoft.
It has filed a similar complaint with German anti-trust authorities and is working with our coalition members in France to file a complaint there.
Frank Karlitschek, chief executive and founder of Nextcloud, said: "This is quite similar to what Microsoft did when it killed competition in the browser market, stopping nearly all browser innovation for over a decade.
"Copy an innovators' product, bundle it with your own dominant product and kill their business, then stop innovating. This kind of behaviour is bad for the consumer, for the market and, of course, for local businesses in the EU.
"Together with the other members of the coalition, we are asking the anti-trust authorities in Europe to enforce a level playing field, giving customers a free choice and to give competition a fair chance.