Is it necessary to wear a white shirt inside the graduation gown for Masters degree graduation ceremony?
Faculty do not ask and students do not tell what they wearing under the robes. 

Actually, I find that since graduations are in May, the robes are often swelteringly hot (especially PhD robes) in many parts of North America, so the lighter the clothes and the more sweat-resistant and breathable the better. Women can get away with wearing summer dresses. From what I can ascertain (remembering the Don't Ask/Don't Tell rule above), male students tend to wear khakis and comfortable dress shirts underneath. No need to wear long-sleeves if it's going to be hot.

Many students often change into other clothes for the receptions after graduation -- men into longer pants and a sport jacket, women don a light jacket or change into more formal attire. They often keep a change of clothes in their parent's car or in their advisor's office if the dorms are shut.

tl;dr: It's your graduation. No need to be uncomfortable.