He pleaded guilty to 12 counts of using a document to obtain a pecuniary advantage and three counts of providing false information.
Singh is the first MSD investigator to be prosecuted for welfare fraud.
The conviction is highly embarrassing for the MSD, which says Singh's offending was a "highly unusual fraud perpetrated by someone who was in a unique position of trust".
"It is particularly disappointing for us that someone entrusted with this responsibility has been convicted of committing serious fraud of this nature," said Ruth Bound, deputy chief executive of the Ministry.
The fraud was uncovered after an anonymous call to the Ministry's benefit fraud allegation line in January 2013.
Bound said detecting fraud by staff can be challenging because of their "insider knowledge".
"We have no doubt that a fraud like this one would eventually be exposed because of the multiple system checks we have in place.
"Since this offending occurred we have put in place a range of additional measures that mean someone in Mr Singh's position would not be able to commit these offences in this way today."
- Additional reporting: Melissa Nightingale