I agree with others who have expressed surprise that you didn't just say something to begin with - "Oh wow, what happened to your hand, are you okay?" Those are the first words that would come out of my mouth with friends of any level (or even probably just acquaintances, depending on circumstances).
In the more general situation you describe, I'd do exactly the same - my instinctive question of what happened, are you okay? If they brushed it off or said they not want to discuss it, I would follow their lead. Only if I repeatedly noticed bandages, bruises, cuts, whatever over a period of weeks or months would I say anything more.