The desktop's "Share Across Computers" feature stores web browsing history, Microsoft Office documents, PDF and text files on Google servers so a user can run remote searches for them on multiple computers.
But EFF said it fears government intrusion and cyber attacks could result.
"(We urge) consumers not to use this feature, because it will make their personal data more vulnerable to subpoenas from the government and possibly private litigants, while providing a convenient one-stop-shop for hackers who've obtained a user's Google password," the EFF said in a statement.
A Google spokesperson could not immediately be reached for comment this afternoon.
However, the EFF quoted the company as saying, "We store this data temporarily on Google Desktop servers and automatically delete older files, and your data is never accessible by anyone doing a Google search."
According to the EFF, Google said users could use a "clear my files" button to manually remove all files from company servers or another preference to remove specific files from the software's index.
On Thursday, the search engine giant launched Google Desktop 3 Beta, saying the updated version allows users to more easily find and share information.
Of its "Share Across Computers" feature, Google said: "It helps users easily access information from all of their computers, so they don't need to remember where all of their documents are organized or filed."