A print-out of the song was seen by a man at a Jobcentre in Birkenhead
Staff at a Jobcentre who circulated an alternative version of The 12 Days of Christmas mocking the unemployed are to be investigated.
The song, which was passed around by email, ends each verse with the refrain: "And a scally in a hoodie."
A print-out was seen by an unemployed man at a Jobcentre in Birkenhead, Merseyside, who was reportedly told the joke was helping staff morale.
Employment and Welfare Reform minister Tony McNulty has ordered an inquiry.
He said: "These comments are in no way representative of the attitude of the vast majority of Jobcentre Plus staff who work very hard to support our customers.
'Nine screaming babies'
"We have very clear rules for staff about the use of potentially offensive material, and this is clearly offensive.
"I will get the matter investigated and will take appropriate action if necessary."
THE STAFF'S ALTERNATIVE GIFTS
Twelve hunting rifles
Eleven spotty youths
Ten fleas a-leaping
Nine screaming babies
Seven recovering alcoholics
Five direct payments
Four Fresh Starts
Three crisis loans
Two missed EVs
And a scally in a hoodie
The verse of the song, titled 12 Days at Brunswick - a reference to the Jobcentre building - substitutes the real gifts delivered by the song's true love.
On the first day at Brunswick the author is sent a "scally in a hoodie" rather than a partridge in a pear tree.
The second brings "two missed EVs" - evidence claimants bring in to prove they should receive benefits.
The third day of Christmas brings crisis loans; the fourth Fresh Starts - a scheme to help the long-term jobless find work.
The fifth day brings direct payments; the sixth "DMAs", which are Decision Maker Actions, what the staff decide to do.
Recovering alcoholics are the seventh day's gift with P45s following the next day.
Day nine sees "screaming babies" come to the Jobcentre with "fleas-a-leaping" on the tenth.
Spotty youths are in abundance on Christmas's eleventh day and "hunting rifles" are the gift on the final day.