You can register your marriage with Indian embassy or consulate in Singapore under provisions of foreign marriage act 

o,
The Marriage Officer
Consulate General of India 
Singapore 
Dear Sir,
Date: _________
I, ________________, d/o of _______________, holder of Indian Passport No._____________, currently resident at _______________________, got married to Mr. _______________, an ____________ national, on_________,______. I wish to get our marriage registered under section 17 of the Foreign Marriage Act.
It is requested that a Certificate of Registration of Marriage may kindly be issued to me. Copies of our respective Passports are enclosed.
Sincerely
(Applicant)

You have to register your marriage under the provisions of special marriage act in India as per prescribed procedures.

You can visit jurisdictional marriage Officer to clarify the details of all the requirements.

You need to register your marriage under Foreign Act, 1969. Approach the Marriage Officer of Indian Embassy and make a written application for registration of marriage under FMA. Upon payment of prescribed fee your marriage will be registered. Marriage Office will enter a certificate  of marriage in the Marriage Certificate  Book, the parties to the marriage need to sign the certificate  of marriage with three witnesses. After these formalities your marriage is valid in India.

Marriage in India is required to be registered under Indian marriage law. If a marriage between an Indian and a foreign national is to take place in India, the marriage has to solemnize under the Special Marriage Act of 1954.Generally, you are required to file a notice of intended marriage with a Marriage Registrar of your choice in India. This notice is required to be published within the stipulated 30 days. At the end of the 30 days the Marriage Registrar is free to perform the marriage.

If one partner is residing in a foreign country then the partner who is resident in India will have to fill out the “Marriage Notice”  collected from the Marriage Registration Office of his/her choice in India and send it to his/her partner in the foreign country who will also have to fill it out. This “Notice” should then be sent back to the partner in India who will have to re-submit it at the Marriage Registration Office. After the stipulated waiting period of 30 days the marriage can take place in India. Under the Special Marriage Act, 1954 a certificate showing the signatures of the persons married, the registrar and the witnesses will be issued. This Certificate is required as proof of marriage and when applying for a visa to a foreign country.

The requirements for this will be your age proof (Passport, Birth Certificate), your address proof (Passport, Ration Card, Voter Identity card) and Martial status. The best for you both to give one notice of marriage under the Act of 1954 to the Marriage Officer of the District where you permanently reside in India, after one month notice period marry her in the presence of 3 witnesses by the Marriage Officer, get Valid Marriage Certificate from the Marriage Officer.

Otherwise, you can apply in India at the time of arrival at home in India. Your marriage has to be solemnised under the Special Marriage Act of 1954. However, one month of notice for the registration of such marriage has to be given and after no objection to registration raised, then only marriage is registered under the Act of 1954.

Additional documents to be presented to the Indian authorities are usually:

• Your valid Passport
• Original Birth Certificate showing both your parents' names
• if a fiancé is widowed, the original death certificate of the deceased spouse
• if divorced, copy of the final divorce decree

Note 

If one partner is residing in a foreign country then the partner who is resident in India will have to fill out the “Marriage Notice”  collected from the Marriage Registration Office o in India and send it to his/her partner in the foreign country who will also have to fill it out. This “Notice” should then be sent back to the partner in India who will have to re-submit it at the Marriage Registration Office. After the stipulated waiting period of 30 days the marriage can take place in India. Under the Special Marriage Act, 1954 a certificate showing the signatures of the persons married, the registrar and the witnesses will be issued. This Certificate is required as proof of the marriage and when applying for a visa to for a foreign country.

You can show that registration and make it admissible in India. You don't have to again register the same in india

- Since, your husband is an Indian , then the marriage can be registered in India under the Special Marriage Act. 

- However, you can even registered under the Foreign marriage Act in Singapore as well with the assistance of Consulate of India ,and that marriage will be valid in India and no registration is required in India after this. 

- If you want to register the marriage in INDIA , then your presence for at least 30 days is required in INDIA. 

- The following documents are required :

1. Birth certificates (for age proof)
2. A valid visa of more than 30 days for the foreign national
3. A single-status affidavit signed by both parties. In case one of the parties has married previously, the Divorce Decree (for divorcees) or Certificate of Death (for widowed) is necessary.
4. Address proof and passport size photographs
5. Adequate documentary evidence of 30-day residence in India
6. A ‘no-objection’ letter from the Malaysian Embassy or Consulate, 
7. Three witnesses are required, who have to provide passport sized photographs, as well as identification and proof of address

Dear client, you can apply through Embassy