Picasa for Linux isn't a native Linux application and instead, it uses WINE which comes bundled with it (so the user doesn't have to install WINE), though it does have some tweaks to make it integrate better with Linux. Well, even this Wine Picasa for Linux has been deprecated by Google.
Users who have already downloaded Picasa for Linux can continue to use it, but there will be no further updates and also, Picasa for Linux can no longer be downloaded it via http://picasa.google.com/. For now, the application is still available in the Google Ubuntu repository though.
We launched a WINE-based version of Picasa for Linux in 2006 as a Google Labs project. As we continue to enhance Picasa, it has become difficult to maintain parity on the Linux version. So today, we’re deprecating Picasa for Linux and will not be maintaining it moving forward. Users who have downloaded and installed older versions of Picasa for Linux can continue to use them, though we won’t be making any further updates.
The last Picasa for Linux version is 3.0, while Picasa for Windows has already reached version 3.9 and even though the Windows version is not officially supported on Linux, you can still use it and even get the Google+ integration working - see our Install Picasa 3.9 In Linux And Fix Google Sign In Issue [Wine] post for more info.
Thanks to Emmet McPoland for the tip!