The blood of kings is more effective than rabies دِمَاءُ المُلُوكِ أَشْفَى مِنَ الكَلَبِ.

The root of the word "rabies" is severity, and "the dog of winter" refers to its intense cold. A "rabid dog" is one that is rabid and eats human flesh. It is narrated that "the blood of kings is the cure for rabies." The Arabs believed that whoever suffered from rabies due to the bite of a rabid dog—a condition akin to madness that afflicts one after such a bite—would be cured if given the blood of kings to drink. Some scholars of interpretation refuted this, saying that the proverb means that the blood of a noble person is the quenching of thirst for revenge, as the poet said: "A rabid dog, from the pain of what has befallen him... and the anxieties of a bewildered heart." And as it was said: "A rabid dog, striking skulls and necks..." They said: So, if someone is rabid with rage and anger, and then achieves their revenge, that is the cure for the rabies, not that there is actually blood being drunk.
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The proverb "The blood of kings is more healing than rabies" does not literally refer to drinking blood, but rather to someone whose anger and grief are only soothed by taking revenge on a powerful figure or the one who caused them harm. "Rabies" here refers to intense anger and agitation, and "healing" means quenching the thirst for vengeance.
There is no English proverb that is a direct equivalent, but some of the closest proverbs and expressions are:
Revenge is sweet.
Nothing heals like revenge.
Vengeance is a balm to the wounded soul.
The best revenge is satisfaction.
The best revenge is achieving satisfaction and quenching the thirst for vengeance. If you want an English proverb that closely resembles the spirit of the Arabic proverb, the best equivalent is:
Revenge is sweet.
However, if you want to preserve the meaning of "quenching anger by taking revenge," the more accurate expression is:
Nothing soothes wrath like revenge.
That is, nothing extinguishes anger like revenge.
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أصل الكَلَب الشدَّةُ، وكلبة الشتاء: شدة برده، والكَلب الكَلِب: الذي يَكْلَبُ بلحوم الناس، ويروى "دماء  الملوك شِفَاءُ الكلب" تزعم العرب أن مَنْ كان به كَلَب من عَضِّ الكَلْب الكَلِب - وهو شيء شبيه بالجنون يعترى من عضة ذلك الكلب - ثم إذا سقي دماء الملوك شفي، ودفع بعضُ أصحاب المعاني هذا، فقال: معنى المثل أن دمَ الكريم هو الثأرُ المُنِيمُ، كما قال القائل:
كلبٌ من حس ما قد مسه ... وأفانين فؤاد مختبل
وكما قيل: كَلِبٌ بِضَرْب جَمَاجم ورِقَابِ ...
قال: فإذا كلب من الغيظ والغضب، فأدرك ثأره فذلك هو الشفاء من الكلب، لا أن هناك دَماً يُشْرب في الحقيقة.