Could this sentence also be translated as "I will read that book by Wednesday."?
"by" is attached to "Wednesday," not to "read." Here "by Wednesday" means "before Wednesday." You can use many other verbs this way, for example "He will go there by next week," or "I will finish this by the end of the day" (a common phrase to say at work).
Another variant - "i will have this book read by Friday" , but it is not accepted. Boo on you!