The US government says it shutdown the Anonymous hackers within 90 minutes of detecting the intrusion.
The hack was mounted by a group operating under the Anonymous banner on July 24. More than 4,200 people's data are thought to have been compromised.
Anonymous is a brand used by fragmented groups of hackers.
It was originally unclear how the hackers managed to steal the data.
However, Census Bureau director John H. Thompson revealed how the hackers breached the department's systems in a blog post.
"Earlier this week, the Census Bureau experienced an attack to gain access to the Federal Audit Clearinghouse, which is housed on an externally facing IT system that contains non-confidential information," read the post.
"It appears the database was compromised through a configuration setting that allowed the attacker to gain access to the four files posted to the hacker's site."
The Federal Audit Clearinghouse is a database used by the Census Bureau to collect audit reporting packages from state and local governments, non-profit organisations, and Indian tribes expending Federal awards.
Thompson said the hackers never managed to breach the Census Bureau's internal systems, or steal any sensitive data.
"The hackers acquired the data illegally, but [...] the Clearinghouse site does not store any confidential household or business data collected by the Census Bureau," read the blog.
"That information remains safe, secure and on an internal network segmented apart from the external site and the affected database."
He added the Census Bureau's IT team was able to shut the hackers down within 90 minutes of detecting the intrusion.
"Within 90 minutes of learning of the breach, we made the system inaccessible. It will remain offline until we can complete our thorough investigation and take steps to ensure the systems integrity in the future," read the blog post.
The Census Bureau breach follows a larger attack on the US Office of Personnel Management (OPM).
The White House revealed the attack in June when it admitted hackers had breached the Office of Personnel Management (OPM), compromising the details of roughly four million staff.