In standard English, we would say "My master said, 'Invite the young lady to go riding'." From what I have found about this story, the speaker of this sentence is probably young, and probably a speaker of non-standard English, or even just learning English. (Look at the other things this character says.)
There are three examples of non-standard English in the first four words. Some varieties of English use present tense more than past tense: "My master says, 'Invite the young lady ...'." (This sentence is possible even in standard English.) Some varieties don't use third-person '-s: "My master say, 'Invite the young lady ...'." Some varieties use a pronoun after the noun: "My master, he say, 'Invite the young lady ...'."
So the writer is using non-standard English to tell us something about the character.