In a statement, the company says it was "aware of a flaw in Java software integrated with web browsers."
The glitch is only in the JDK7 version of the software and the company says it "does not affect Java applications directly installed and running on servers, desktops, laptops and other devices."
Oracle adds "A fix will be available shortly."
The DHS had advised people to temporarily disable the Java software on their computers to avoid potential hacking attacks. Computer security experts believed hackers had found a flaw in Java's coding that creates an opening for criminal activity and other high-tech mischief.
Java is a widely used technical language that allows computer programmers to write a wide variety of Internet applications and other software programs that can run on just about any computer's operating system.