Verdict: No
No. SQL Server Management Studio runs only on 64-bit Windows according to Microsoft's own requirements. You can still reach your SQL Server databases from Linux using DBeaver instead.
Microsoft's system requirements for SSMS 22 list 64-bit Windows 11 and Windows Server 2019, 2022 and 2025. There is no Linux or Mac version, and SSMS is now installed through the Visual Studio Installer, which is itself Windows software. It also needs .NET Framework 4.8, another Windows piece. None of this travels.
The good news is that the databases do. SQL Server speaks a network protocol that any operating system can use, so the server can sit on Windows while you connect to it from Linux. DBeaver Community is free, is in the Linux app store, and connects to SQL Server along with MySQL, PostgreSQL and most others. For browsing tables, writing and running queries, editing rows and exporting data, it covers what most people actually did in SSMS. Microsoft's own mssql extension for VS Code is another option if you already live in that editor.
What you lose is the administration side. Maintenance plans, SQL Server Agent jobs, the security dialogs, Integration Services packages and the rest of Microsoft's management tooling are not reproduced by DBeaver. If your job is running and maintaining a SQL Server rather than querying one, keep a Windows machine for those tasks.
Files are barely an issue. A .sql script is plain text and opens anywhere. Saved connection settings and any .sqlproj database projects do not transfer, so write down your server names, ports and authentication details before you wipe Windows, and set them up again on the other side.
Free, in the app store, and connects to SQL Server from Linux. Covers querying, browsing and editing data well. Does not reproduce SQL Server administration screens.
Your files: Opens .sql scripts, which are plain text. Saved SSMS connections and .sqlproj projects do not transfer.
With Microsoft's own mssql extension it connects to SQL Server and runs queries. Lighter than DBeaver and better if you already work in VS Code.
Your files: Opens .sql scripts. No support for SSMS project files.
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 SQL Server Management Studio. Everything else you do can move.
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