MediLexicon clearly states that injecting air bubbles into the bloodstream can lead to brain damage or even death if the air bubble is able to cut off the supply of blood to the brain. The presence of air in the bloodstream is referred to as an air embolism.
Wikipedia mentions two types of air embolisms, venous and arterial, stating that an arterial air embolism is far more dangerous than a venous embolism. While a venous embolism involves air making its way to the heart through a vein, an arterial embolism involves the movement of an air bubble through an artery. Healthline explains that in both types of air embolisms, a large amount of air is required to cause any damage or death.