Ebosse, 24, is reported to have been struck in the head by a projectile following JS Kabylie's 2-1 home Algerian Ligue 1 defeat to USM Alger, in which he scored a 27th-minute penalty for the hosts.
In a statement, his club said: "The Ministry of Interior and Local Government, through minister Tayeb Belaiz, has given the instruction to open an investigation into the circumstances surrounding the death of Albert Ebosse.
"The JSK player succumbed to a head injury after being hit in the head at the end of the meeting with USM Alger."
Opponents USM Alger also expressed their sympathy for the player's family in a release on their official website.
"JS Kabylie's Cameroonian striker has lost his life after being hit in the head by something launched from the stands," it read. "This terrible news is saddening for football in our nation and in Cameroon and arrives like a bombshell just hours after the meeting with USM Alger which was played in Tizi Ouzou.
"In these painful circumstances, USM Alger and its members send their deepest condolences to the family of the deceased and to JS Kabylie. May Albert Ebosse rest in peace."
Addressing the incident, CAF president Issa Hayatou was strong in his condemnation of all violence in African football.
"My thoughts go out to the family and friends of this young man who enjoyed his job peacefully and went further to pursue his passion for football abroad," he said. "African football cannot be the breeding ground for hooliganism whatsoever.
"We expect exemplary sanctions to be taken against this grave act of violence.
"Violence has no place in African football in particular and sports in general.
"We remain resolute and state in the strongest terms our determination to eradicate all forms of violence and unsportsmanlike conduct in stadiums on the continent."
Striker Ebosse was the top scorer in the Algerian top flight last season, scoring 17 goals as JS Kabylie finished second.
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