The video showed the four-time African player of the year breaking free from people trying to hold him down and kneeing the blogger, named Sadouni SM, in the face.
The man fell backwards after being hit.
Eto’o has walked away and has not commented or been seen since.
A Cameroon FA official said former Barcelona striker Eto’o did not want to talk about the incident.
The African football legend found himself surrounded as soon as he left the 974 Stadium where the round of 16 was played.
Wearing a blue baseball cap, he is seen taking selfies with some fans before being approached by the Algerian.
It is not known what comment was made, but Eto’o handed his mobile phone to a man before pushing the blogger into kneeing him.
Sadouni SM said in a video posted online Tuesday that his camera and microphone had been “broken” in the incident.
“He hit me,” the man adds, pointing to his chin.
Cameroon beat Algeria on away goals in a World Cup qualifier this year and then Algeria sentenced the referee.
“I did all that for Algeria,” says Sadouni SM in the video.
“I am at the police station now for the investigation.
“This video must be shared.
Since Eto’o is a celebrity, I am afraid they will cover up the investigation, but I trust the Qatar police,” he added.
Qatar’s World Cup organizing committee did not immediately comment on the incident.
Eto’o toured Senegal, Cameroon and Ghana in August to promote the World Cup. The former international has a history of outbursts of fire, having received a three-math ban in 2010 for headbutting an opponent while playing for Inter.