It's Kino's wife Juana who injures her hand while trying to protect their baby Coyotito from the scorpion. She smashes the scorpion with a rock, but in doing so, she also breaks her hand.
The injury to Juana's hand is a significant moment in the story as it symbolizes the sacrifices and hardships that Juana is willing to endure for her family, and it also serves as a catalyst for Kino's actions to find the pearl.