Slack says Microsoft illegally bundles the Microsoft Teams messaging product, which is similar to Slack, into Office 365, its package of email and other widely used business software.
Slack says Microsoft forces companies to install it for millions and blocks its removal.
Slack Technologies Inc, which went public in 2019, has been growing rapidly.
It reported 201.7 million dollars (£158 million) in sales in its February-April quarter, up 50% from the same time last year.
It also reported 122,000 paid customers, up 28% from when the company went public in April 2019.
Slack still faces tough competition, particularly from Microsoft’s Teams software.
Slack last month announced an expanded partnership with Amazon’s cloud computing division, an attempt to join forces with Microsoft’s chief rival.
It more recently announced it is buying Rimeto, which creates detailed staff directories.
The European Commission will review the complaint and decide whether to open a formal investigation.
