The natural, everyday way to say this is "I need to be excused from class." If the student didn't mention this to the teacher, one can imagine a conversation like this: Teacher: "You were absent yesterday. What's your excuse?" Student: "I had a doctor's appointment." Teacher: "Do you have a note from the doctor?" Student: "Yes, here it is." Teacher: "That's a valid excuse. Ok, I will excuse [S pronounced like Z] you this time. But in future, please come to me before the appointment and get permission first." So we have the noun "excuse," with the S pronounced the normal way. It can mean either the reason (the doctor's appointment) or the permission. And we also have the verb "to excuse," meaning "to give permission," with the S pronounced like Z.

Be excused from

It depends on the circumstances. If this is a compulsory English class that you must attend, I'd say, "I have a doctor's appointment (tomorrow). Is it OK if I miss (tomorrow's) class / if I'm late for (tomorrow's) class?" If the class is optional and you don't really need your teacher's permission to miss it, I'd say, "I have a doctor's appointment (tomorrow) so I'm afraid I won't be able to make (tomorrow's) class / I'll be late for (tomorrow's) class.

You could say “I need to ask for leave from my class.”

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