The bug was first reported on Monday after going undetected for more than two years. It bypasses the OpenSSL cryptographic library, which is used online to digitally scramble sensitive information as it passes between computer servers.
It is best known as the padlock icon that appears in the corner of web browser windows to show the page you are using online is secure when data moves back and forth.
The Heartbleed bug is a flaw in this system that can give anyone access to the data behind that encryption, including passwords and credit card details, without leaving any trace.
Popular blogging site Tumblr, part of Yahoo!, has since posted a warning to its users, encouraging them to update all of their existing passwords.
"This might be a good day to call in sick and take some time to change your passwords everywhere - especially your high-security services like email, file storage and banking, which may have been compromised by this bug," said the post.
Codenomicon, a cyber-security research group, has set up a dedicated website giving information on the bug; heartbleed.com, and said: "The Heartbleed bug allows anyone on the internet to read the memory of the systems protected by the vulnerable versions of the OpenSSL software.
"This compromises the secret keys used to identify the service providers and to encrypt the traffic, the names and passwords of the users and the actual content.
This allows attackers to eavesdrop on communications, steal data directly from the services and users and to impersonate services and users."
However, the online security firm were also quick to acknowledge a positive within the discovery of the flaw: "For those service providers who are affected, this is a good opportunity to upgrade security strength of the secret keys used."
"For those service providers who are affected, this is a good opportunity to upgrade security strength of the secret keys used. A lot of software gets updates which otherwise would have not been urgent. Although this is painful for the security community, we can rest assured that infrastructure of the cyber criminals and their secrets have been exposed as well."