These two virtual spaces were set to be active during the same time but were in separate Zoom calls.
Legal and policy director of the American-Arab Anti-Discrimination Committee, Abed Ayoub, told the Daily Mail he understood the intention but said it could have been done differently.
Ayoub told the Daily Mail it is important for white students to learn from the experiences of students of colour.
Ayoub flagged the event postings yesterday on Twitter.
"From U of M - Dearborn. The Non-POC Cafe or the 'White Cafe'," wrote Ayoub.
"Anyway, I wonder what the menu looks like for the Non-POC Cafe at UM-Dearborn. If they have chocolate hummus I am calling for a boycott."
In a statement, the university apologised for referring to the online gatherings as "cafes", saying they weren't intended to be exclusive or exclusionary for individuals of a certain race.
Using the word "cafe" caused confusion because people thought the university was building two physical cafes, the vice-chancellor said.
"The terms used to describe these virtual events and the descriptions themselves were not clear and not reflective of the university´s commitment to diversity, equity and inclusion," the university's statement said.
The statement also explained that the "cafes" were meant for students to "process current events" related to race.
"The 'cafes' were virtual open conversations developed to allow students the opportunity to connect to process current events, share their experiences related to race, share knowledge and resources and brainstorm solutions.
"The original intent was to provide students from marginalised communities a space that allowed for them to exist freely without having to normalise their lives and experiences, while also providing students that do not identify as persons of colour the opportunity to deepen their understanding of race and racism without harming or relying on students of colour to educate them."