The Ohio Department of Job and Family Services said about two dozen people had the ability to view other people's information who applied for the Pandemic Unemployment Assistance (PUA).
ODJFS said there is no evidence of widespread data compromise.
The agency said it was notified over the weekend by the company that developed the system, Deloitte Consulting.
Multiple people contacted 10TV providing the email they received from ODJFS warning them that their name, Social Security number and street address could be viewed.
The email also said there was no indication people's information was improperly used.
ODJFS said the issue was fixed within one hour and it contacted those who had accidental access to system data.
The agency said in a news release, "Deloitte is offering credit monitoring to all PUA claimants for 12 months. ODJFS holds the confidentiality of claimant data in the highest regard and agreed with the immediate steps Deloitte took to prevent any unauthorized PUA access in the future."
Pandemic Unemployment Assistance allows for up to 39 weeks of benefits to those who are self-employed, part-time workers or 1099 tax filers.
A Deloitte spokesperson said in an e-mailed statement, "“We are deeply committed to protecting the personal information of our clients and the people they serve. The system was not breached. A unique circumstance enabled about two dozen Pandemic Unemployment Assistance claimants to inadvertently access a restricted page when logged into the state’s PUA website. Within an hour of learning of this issue, we identified the cause and stopped the unauthorized access to prevent additional occurrences. Out of an abundance of caution, we are offering 12 months of free credit monitoring to those PUA claimants potentially impacted.”"