English Translation
I hurt my foot.
What’s wrong with “Ich habe meinen Fuß verletzt.” ?
Short explanation: It’s less idiomatic 
Your version sounds like the foot isn’t part of the body, just something you own. It would sound ok if it’s about your cat or dog, but not with your own body parts.
Hurting is reflexive (“sich verletzen”), even if it’s an accident and not on purpose. You could also say “Ich habe mich am Fuß verletzt” (= “I hurt myself in the foot.”). So if you don’t use “mich” (accusative) directly, you need at least “mir” (dative) to make it sound right.
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If you’ve hurt yourself, you need to add “mich”.
- Ich habe mich verletzt.
- Er hat sich verletzt.
- Hast du dich verletzt?
If you hurt someone else, you don’t use such a reflexive pronoun.
- Das Kind verletzte seine Mutter als es ihr sagte “Ich hasse dich.”
- The child hurt its mother when it said to her “I hate you”.
If you say “Ich habe meinen Fuß verletzt”, it sounds as though your foot weren’t a part of you, like @pitti42 wrote.
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This pattern with an indirect (dative) object and a direct (accusative) object with definite article is pretty common in german, where english often only uses the direct object together with a possessive pronoun.
We already had some examples in another thread (Er schaut sich jeden Morgen die Nachrichten an. - #2 by pitti42).
In that thread, I claimed that the (reflexive) dative expresses “to do myself a favor”, but as we can see here, it also can be an accident or bad things in general.
So, the dative in general expresses “what you do to/for someone”:
Ich habe mir die einzige Chance versaut. - I effed up my only chance.
Er macht mir das Leben zur Hölle. - He makes my life a living hell.
Ich werde ihr den Tag versüßen. - I will sweeten up her day.
Ich massiere ihm den Nacken. - I’m massaging his neck.
Ich werde dir die Fresse polieren. - I’ll smash your face! (“I’ll polish your piehole!”)
Er nahm ihr die Tasche ab. - He took the bag from her. (as a courtesy, so she doesn’t have to carry it)
Kannst du mir die Flasche öffnen? - Can you open the bottle for me?
Ich kann dir die Flasche öffnen, wenn du willst. - I can open the bottle for you, if wou want.
So, in the case of “Ich habe mir den Fuß verletzt”, it’s like “What I’ve done to myself is hurt my foot.”
Now I get it. Collecting body parts is obviously a popular hobby in Germany so, when I say “my foot” it might not be the foot attached to my leg but part of my body part collection.