Singh was working on the merchant vessel Gulf Dove.
INS Tarkash, which evacuated about 450 people from Aden harbour on Friday, is carrying his body to Djibouti.
Government sources said the exact dates of his injury or death have not been confirmed so far.
India had on Thursday concluded its air evacuation operations from Yemen, rescuing another 630 of its citizens from Sanaa and taking the total number of Indians brought home from the war-ravaged country to over 4,640. India has also evacuated around 960 nationals from 41 countries.