A shot by team-mate Ogenyi Onazi struck Babatunde's hand during the 3-2 loss, but Nigeria still reached the last 16.
Nigeria coach Stephen Keshi confirmed the 21-year-old Volyn Lutsk midfielder required surgery.
"I think he's got a broken hand and he's going for surgery right now as we speak," Keshi said.
"So I'm not sure if he's still going to participate in this World Cup, but we'll see how he goes.
"It's not good."
African champions Nigeria face France in the round of 16 in Brasilia on Monday.
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