No. Adobe XD is a Mac and Windows program with no Linux version, and Adobe has placed it in maintenance mode, meaning it is no longer being developed.
Adobe XD by Adobe · Design, CAD & 3D · No way to run it
Adobe's own help pages carry a notice that Adobe XD is in maintenance mode. It still exists for Mac and
Windows through Creative Cloud, with companion mobile apps for previewing designs, but it is not getting
new features and there has never been a Linux build.
That changes how you should think about this one. Even users staying on Windows are being pushed to move
off XD, so switching to Linux is a reason to change design tool rather than a reason to hunt for a
workaround.
Penpot is the closest replacement that runs on Linux. It works in a browser, it is free and open source,
and it covers designing screens, building component libraries and sharing clickable prototypes with other
people, which is most of what XD was used for.
Your old .xd files are the sore point. Nothing on Linux opens them properly. While you still have the
Windows machine, open your important documents in XD and export what you need, as SVG for artwork that
needs to stay editable and as PDF or PNG for records. Layered editable structure will not survive the trip,
so keep the exports organised and expect to rebuild anything you intend to keep working on.
Free and open source screen design and prototyping in a browser, so it runs on Linux with nothing to install. The tools are arranged differently and it is not as fast on huge files.
Your files: Cannot open .xd files. Imports SVG artwork you export from XD first.
Installed, free, and good for icons, logos and illustration. It is a drawing program, not a prototyping tool, so clickable prototypes are out.
Your files: Cannot open .xd files. Opens SVG and PDF exports well.
This doesn't have to stop you
One stubborn program doesn't have to decide the whole question. You can keep Windows on the same PC and restart into it only when you need Adobe XD. Everything else you do can move.