Many in the Arabic community believe the incident was motivated by race and religion, saying it should be treated as a hate crime.
A local shopper said she heard slurs like "Terrorist" "Rag-head" and "Go back to your country" before two white men started punching an Arab-American man at the store.
"So when this came about, the question was was this racially motivated is this another attack on Muslims," said Osama Siblani, publisher of the Arab-American News.
Investigators are working to find what sparked the alleged assault of the man shopping with his children.
Kathy McMillan Bazzi claims to have witnessed the assault and wrote on Facebook two white men were passing by and started to make derogatory comments about Isil.
before suddenly punching the Arab man.
All of it said to have happened in front of the victim's children.
"They've just been sworn at as Isil, as Muslims, as 'Take your rag off from your head' it seems like it's a hate crime," said Sufian Nabhan.
The incident is said to have started with racial slurs
Siblani believes the alleged assault is a hate crime but he's calling for calm.
"People should not make assumptions," he said. "They should not draw conclusions and they should not spread hearsay.
"I want an official statement, I want to see whether the police can see what I see."
Dearborn police released this statement Friday.
"The incident is currently being thoroughly investigated to determine whether it involves a criminal assault and/or whether it was motivated, in whole or in part by, the offender(s) bias."
So far no one has been arrested.
A Kroger spokesman says the two suspects left the store before police arrived.
"Reading the statement you just gave me, it absolutely looks like a hate crime," said Ibrahim Elkadir.
And to many, it seems it's happening more often.
The Kroger incident happened a night before investigators say someone intentionally set part of a Houston mosque on fire.
And it follows the tragedy in Chapel Hill, North Carolina where police say 46-year-old Craig Hicks, who is white, gunned down three Muslim-American students.
While police believes the killings stemmed from an ongoing parking dispute, most Muslims believe the victims were targeted because of their religion.
Tonight many believe what happened in Dearborn was no different.
Police Chief Ronald Haddad said that his department will have full disclosure of the incident once it has been investigated.
Kroger officials said Dearborn police were at the store reviewing security camera footage Friday.
Dearborn police have also reached out to state and federal law enforcement agencies to assist in the investigation.