The picture was in fact one of British doctor and convicted killer Harold Shipman, who murdered up to 250 people.
Twitter users quickly told Mr Dunne of his mistake, and the minister deleted his tweet.
The trick appeared to have been a copy of a similar prank played on US business mogul Donald Trump, who was asked to retweet a picture of British serial killers Rose and Fred West.
After realising his error, Mr Trump threatened to sue the prankster.
Mr Dunne was more forgiving. He later tweeted: "I thought the photo looked familiar - a most unfortunate start to the day. Mea culpa".
William Guy said the minister was "a good sport", adding: "I've just got to keep politicians on their toes."