It all depends on what area of humerus bone is fracture whether it is near the shoulder or near the elbow or in the middle Also whether it is displaced or not Now a days usually to avoid problems of stiffness and if the fracture is displaced it is better to operate so that you can be free of the plaster earlier and can get a better result However if the fracture is not displaced then maybe only plaster for 4-6 weeks is good and then maybe a month of good physiotherapy and exercises But to get a true opinion post your Xray photo

Completely agree with Dr Saakshi Dhingra.

At least 4 to 6weeks needed....Wld take 2months of exercising at least post plaster removal for recovery