Is it correct to say that book was written by I?

No, it is not grammatically correct to say "book was written by I."

The correct way to phrase it is:

"The book was written by me."

"I" is the nominative case pronoun, used for the subject of a sentence. "Me" is the objective case pronoun, used for the object of a verb or preposition.

In the sentence "The book was written by me," "me" is the object of the preposition "by."