It could be due to Sakura's feelings for Sasuke. If she's overly focused on Sasuke and Naruto gets in the way of her plans regarding Sasuke in some way, she might lash out and hurt Naruto without really meaning to cause serious harm.
One possible scenario could be in a fanfic where Sakura accidentally uses her strength during a training session with Naruto and physically hurts him. Maybe she misjudges her punch or kick.
In other fanfics, Naruto might try to understand Sakura's perspective. He's a very forgiving person, so he could give her the benefit of the doubt and try to figure out what made her act in a way that hurt him. He might think that she had her reasons and try to work through it with her.
Well, in some fanfics, Sakura might be jealous of Naruto's growing power and relationship with others. So she could try to undermine him, which in turn hurts Naruto. Maybe she spreads false rumors about him in the village. Another idea is that Sakura is forced to choose between Naruto and Sasuke in a dangerous situation, and her choice, even if it's not completely her fault, ends up hurting Naruto deeply. It could also be that Sakura's overzealous medical treatment, in an attempt to save Naruto from a serious injury, actually causes him more pain and harm.
If Naruto gets hurt by Sakura, their relationship could become strained. Naruto might be confused and hurt, both physically and emotionally. He might start to avoid Sakura at first.
In the fanfic, it might be set in an alternate universe where Sakura has a different personality. She could be more aggressive and competitive with Naruto. During a sparring match, she goes too far and seriously hurts Naruto. This could then be the starting point of a story about Naruto having to forgive her and them rebuilding their friendship.
In many SasuSaku fanfics where Sakura gets hurt, it often leads to Sasuke becoming extremely protective. He might go on a rampage against those who hurt her. For example, in some stories, if Sakura is injured during a battle, Sasuke will use his powerful jutsu to defeat the enemy without mercy. It's a way to show his deep - seated feelings for her that he might not always openly express.
In a hurt comfort fic, perhaps Sakura has an emotional breakdown after a failed mission. Naruto finds her crying alone. He sits beside her and just listens as she pours out her frustrations. Naruto then shares his own insecurities, like how he sometimes doubts if he can really become Hokage. This mutual sharing of pain and comfort brings them closer, strengthening their friendship in a way that goes beyond their ninja duties.
In some fanfictions, Sakura might accidentally hurt Naruto during a training session. Maybe she uses a new jutsu she's not fully mastered and it goes wrong, hitting Naruto instead of the target.
One common theme is misunderstanding. Often, Naruto may misunderstand Sakura's intentions or vice versa, which leads to one of them getting hurt. For example, Naruto might misinterpret Sakura's concern for him as pity, and his reaction could hurt her.