Should I drink a protein shake after cycling?

No, drinking a protein shake after cycling isn’t necessary, however, many athletes find it useful for recovery. Research indicates that consuming a combination of carbohydrates and protein post-ride accelerates recovery by replenishing glycogen stores and boosting muscle protein synthesis. Specifically, consuming 25-40g high quality protein (0.4 -0.5g/kg or 0.9-1.1g/lb) after a ride appears to be ideal [1]. 

Cyclists can get 25-40g of protein from protein-rich foods such as dairy products, eggs, poultry, beef, beans, or tofu, however, you may find it easier to get the same amount of protein from a shake.