Register my oversea marriage in Japan

I need help on my oversea marriage to register in Japan. I am a Malaysian (Singapore PR) married to my Japanese husband in Singapore. We have registed our marriage in Singapore.
How do we register our oversea marriage in Japan?
What are the documents needed?
Do I still need a Single Status Certificate eventhough I already married oversea?
Thanks in advance

Let your Japanese spouse read this:
http://www.mofa.go.jp/mofaj/toko/todoke/koseki/index.html

It will be 3. under "marriages." (This page mainly talks about people living outside Japan.)

When a Japanese national gets married to a non-Japanese national according to the laws of the non-Japanese spouse's country, the Japanese needs to report the marriage, in principle, within three months.

Since you are already married, you will be reporting the Singaporean marriage after-the-fact to the Japanese authorities. So the document you need is the Singaporean marriage certificate (official copy), and its Japanese translation, which your Japanese spouse can make himself.

Are you already in Japan?

I (Japanese national) got married to my EU husband in the UK, and we later returned to Japan. I got myself an extra copy of UK marriage certificate, made a translation of it myself (stating the translator's name), and took it to the city hall of the city we lived in in Japan. There the city hall clerk checked that the marriage certificate was genuine (they had a file with numerous marriage certificate formats from around the world), and registered our marriage into my family register.

Currently I am residing in Singapore. I am planning to register our marriage at Japan Embassy in Singapore.
What about the spouse visa, how do I go about for applying for a spouse visa? Can I apply before going to Japan? What are the procedure and documents needed?
Thanks,

If you are in Singapore, it would be best to ask your husband to ask the Japanese Embassy in Singapore. Since it will be the Japanese national reporting their change of status with the Japanese authorities, he will need to do it anyway.

About spouse visa for Japan: Do the two of you plan to come and live in Japan soon?
If so, you can apply in advance (applying for Certificate of Eligibility), or (if Malaysian nationals can just enter Japan with passport) you can come into Japan together with your spouse, then change your status from Temporary Visitor Status to Spouse of Japanese National.

In any case, the marriage needs to be reported to the Japanese authorities.