I wish that there were as many options for audiobooks as we have in the US through either Audible or our public library Overdrive/Libby system. I am absolutely addicted to audiobooks when they are well read. And when I can switch between or use both at the same time (whisper synch technology) in Kindle, it is wonderful.The information (and wording about Kindle books is here) What you are looking for is to make sure that you have the Audible narration as well as the Kindle e-book. The category is eBooks with Audible. Likewise, another feature that is super interesting for language learners/growing readers is Word Wise, that provides explanations above difficult terms.
I have only found a couple of options that I can access and they aren't nearly as satisfying, but I am still using them. audiobook.jp is one that I have chosen to use. I decided to subscribe to the unlimited version so that I would always have something Japanese to listen to while I am driving or doing tedious work. I have also purchased particular titles that I want to read but know I would never finish (for me that would be light novels). I just finished a lovely long mystery that was so much more fun because of the dialects and honorifics. At some point I will quit subscribing to the unlimited, but at the moment I am still finding plenty to listen to.
Aozora Roudoku 青空朗読 is a fabulous way to read/listen to books/stories that are out of copyright. There are currently (10/2020) 640 titles in this collection. Please note you can browse by length of recording, narrator, genre, title, or author. AND it has an ePub version so that you can have the read while you listen option (always, always my personal recommendation).
I hadn't realized quite how many Japanese audiobooks are available in the US Audible. They are a bit of a bear to find, but using either the genre search and limiting to Japanese or doing a search in Japanese (like by publisher 講談社 文藝春秋 新潮社) you will get quite a list.
I haven't yet figured out why I can't purchase all the titles listed (as in no price or purchase button) but I have a call into Audible to see if they can explain it to me.
There is overlap with audiobook.jp, which is no surprise. Try both and choose whichever works for you.