Here's an answer in 2021 after my research and from my experience living and working in Japan. I like this article, though it is in Japanese so I'll do my best to summarize. Here are what some major companies are using in Japan:
日経 / Nikkei
font-family: "ヒラギノ角ゴ Pro W3","Hiragino Kaku Gothic Pro","メイリオ",Meiryo,"MS Pゴシック",sans-serif;
産経 / Sankei
font-family: "ヒラギノ角ゴ ProN W3","HiraKakuProN-W3","ヒラギノ角ゴ Pro W3","HiraKakuPro-W3","メイリオ",Meiryo,"MS Pゴシック","MS Pgothic","Osaka",sans-serif,Helvetica, Helvetica Neue, Arial, Verdana;
ロイター / Reuters
font-family: "Hiragino Kaku Gothic Pro","Meiryo","MS Pgothic",knowledge-reg,helvetica,arial,sans-serif;
CNN
font-family: "メイリオ", Meiryo, Tahoma, Verdana, "ヒラギノ角ゴ Pro W3", "Hiragino Kaku Gothic Pro", Osaka, "MS Pゴシック", "MS PGothic", sans-serif;
Yahoo JP
font-family: "メイリオ","Hiragino Kaku Gothic Pro",Meiryo,"ヒラギノ角ゴ Pro W3","MS PGothic","MS UI Gothic",Helvetica,Arial,sans-serif;
時事通信 / Jiji Press
font-family: "ヒラギノ角ゴ ProN W3","HiraKakuProN-W3","ヒラギノ角ゴ Pro W3","HiraKakuPro-W3","メイリオ",Meiryo,"MS Pゴシック","MS Pgothic","Osaka",sans-serif,Helvetica, Helvetica Neue, Arial, Verdana;
Note, sometimes it is suggested (such as here) to use a Mincho font stack like:
font-family : 'ヒラギノ角ゴ ProN' , 'Hiragino Kaku Gothic ProN' , '游ゴシック' , '游ゴシック体' , YuGothic , 'Yu Gothic' , 'メイリオ' , Meiryo , 'MS ゴシック' , 'MS Gothic' , HiraKakuProN-W3 , 'TakaoExゴシック' , TakaoExGothic , 'MotoyaLCedar' , 'Droid Sans Japanese' , sans-serif;
Something I learned working here: some Japanese prefer Gothic or other fonts over Mincho fonts, as Mincho looks more "Chinese" according to some. None of the companies above use Mincho as evidence to that. Like it or not, I guess that's something to keep in mind when branding.