According to diplomatic sources, Hugh Johnson of the Protestant Church of Algeria was stabbed by an unknown assailant in downtown Algiers and later underwent surgery.
His condition was not life-threatening, diplomats said.
Police said the investigation to determine any link with terrorism was under way.
Algeria is emerging from more than a decade of violence. Islamist groups began an uprising after the army cancelled a parliamentary ballot in 1992 that an Islamic party was set to win.
More than 150,000 people have since died, according to human rights groups, but violence has fallen sharply in recent years.