Koichi Hagiuda did not give a reason as to why the gift had been rejected.
Japan gave Mr Putin a female Akita called Yume in 2012. This dog was intended as a companion for her.
Mr Hagiuda wrote in a blog post: "Unfortunately, we heard from our counterparts, and our hope to present a bridegroom was dashed."
If accepted, the gift would have been presented to the Russian president at a summit with Japanese Prime Minister Shinzo Abe in Japan next week.
Akitas originate from northern Japan.
