Is there a Linux equivalent to LinqPad?

I have to disagree with the basis of Shauna's answer; LINQPad is not a MS-SQL gui or frontend. It is a .NET scratchpad which can generate a LinqToSql context for supported data contexts. This makes it fundamentally different from typical SQL clients (such as SQL Server Management Studio or MySql Workbench).

Out of the box LINQPad ships with drivers which support MS-SQL, however additional drivers can be easily installed and can add support for other data sources--including MySql.

For your specific question the answer is that the closest think you'll find that can run natively on Linux would be a custom .NET application written with Mono (version 2.6 added LINQtoSql support).

However, if you need to use LINQPad with MySql you easily can using the IQ driver. You will still need Windows to run LINQPad (or, possibly wine). I personally keep a Windows VirtualBox on my Linux development station specifically for a handful of tools such as LINQPad which are windows-only.