Can we say "my hobby is read book"? Is it correct?
In the sense that you mean it, no.
Your example contains is read. If read is the base form (as your question implies), this is not grammatical. [As it happens read is also the past participle of read (pronounced differently: the base form sounds the same as reed, but the past participle sounds the same as red), so is read can be grammatical; but it is passive, so something every night a book is read makes sense. But I don't think this is what you meant.]
What I think you are trying to say is my hobby is reading books. Various things can follow is: a noun or noun phrase, an adjective or adjectival phrase, an adverb or adverbial phrase; but not a verb phrase. The -ing form of verbs acts like a noun, or introduces a clause which acts like a noun phrase. So reading books acts like a noun phrase, and can follow My hobby is.