Sony Corp.’s music unit is set to earn operating profit of more than $1 billion this fiscal year, helping drive the conglomerate to record results. The music unit’s secret weapon: a mobile game called “Fate/Grand Order.”

Ace Research Institute analyst Hideki Yasuda estimates that revenue from the game is likely to top $1 billion in the year ending in March—meaning it brings in an average of more than $2.5 million every day. The game is free to download, but players enthralled by its high-end graphics and storytelling can...