No. Mobatek describes MobaXterm as a single Windows application and publishes no Linux version. Most of what it gave you on Windows is already built into Linux.
MobaXterm by Mobatek · Coding · No way to run it
MobaXterm's own site calls it an enhanced terminal for Windows and a single Windows application. There is
no Linux download, and the Home and Professional editions are both Windows products.
Here is the part people miss. MobaXterm existed largely to give Windows the things Unix systems already
have, an SSH client for connecting to other computers, an X server for showing remote graphical programs,
and a decent terminal. On Linux those are not add-ons. The terminal app that comes with your desktop
connects to remote machines out of the box, and remote graphical programs display without extra software.
What you will miss is the specific convenience of the MobaXterm window, the saved session list down the
side with the file browser next to the terminal. Remmina is the closest thing on Linux for keeping a list
of saved remote connections, including remote desktop sessions as well as SSH, and it comes with several
distributions already.
Your saved sessions do not come across. Export or write down your session list, including host names and
which key file each one uses, while the Windows machine still works. Your SSH keys themselves are ordinary
files and can be copied over.
Keeps a saved list of remote connections including SSH, remote desktop and VNC. The tabbed file browser alongside the terminal is not part of it.
Your files: Does not import MobaXterm sessions. Your existing SSH key files work as they are.
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 MobaXterm. Everything else you do can move.