Drogba limped off after a high 15th-minute challenge by Japan defender Marcus Tulio Tanaka. The Chelsea star could miss the tournament.
"It's an elbow injury, for sure. How bad it is, I don't know. He had a lot of pain," coach Sven Goran-Eriksson said before a team spokesman announced it was a broken arm. "Of course I'm worried. He's our captain and one of the best players in the world."
Eriksson said it was unclear if Drogba was injured by the tackle or landing awkwardly, and did not blame Tulio for the challenge.
"It was unlucky. It wasn't bad or stupid. He didn't want to hurt anyone. Football is a game of contact," the Swedish coach said.
Drogba and Tulio clashed feet high in the air as the Ivorian captain flicked the ball over the defender's head. Drogba refused a stretcher and limped off to be replaced by Seydou Doumbia.
Two minutes earlier, Ivory Coast scored when Drogba's 24-yard free kick was deflected by Tulio into his own net.
Drogba's shot took two deflections, the second off Tulio, to deceive Japanese goalkeeper Eiji Kawashima and bounce slowly into the bottom right-hand corner.
Defender Kolo Toure scored from close range in the 81st minute, meeting a free kick with a crisp shot. A long free kick from the right side was met on the half-volley by Toure with Kawashima stuck on his goal line.
Japan's fourth straight defeat included more own-goal trouble. It conceded two in a 2-1 loss to England last Sunday.
Ivory Coast plays in Group G with Brazil, Portugal and North Korea.
Japan's Group E has the Netherlands, Cameroon and Denmark.