DEL said it had been posted by a bogus company posing as a legitimate employer.
Clients who responded were subsequently asked to pay for criminal record checks, which the bogus firm claimed were provided at a discounted rate agreed with Access NI.
A spokesperson for the department said the vacancy has been removed and the PSNI, Trading Standards Services and the Information Commissioner's Office have been notified.
DEL has also launched an investigation.
They added: "I would like to apologise to the individuals concerned for any distress that this bogus company may have caused.
"The department has contacted all individuals who responded to the bogus company and a helpline has been set up for clients should they wish to get in contact with the department."
Stephen Crooks of the PSNI's Organised Crime Branch told UTV that keeping details secure is vital when online.
He said: "These days your personal details are worth every bit as much as cash because people can go on to open bank accounts in your name, take out credit cards, loans etc.
"The best thing to do is know who you're dealing with by checking their address and checking on the internet to see if there are any complaints about them.
"It's very important to keep your personal details secure."
Anyone who wants more information can contact the DEL helpline on 028 9025 2007.