This has been covered here already: Is the file table in the filesystem or in memory?
That seems to be pretty thorough. But it is still a good question. As you can see, the question is actually more granular than your question suggests.
http://140.120.7.21/LinuxKernel/LinuxKernel/node17.html that's a more technical explanation that seems to cover the same question, with the same answer, there are inode tables in memory and on disk, different types, if I read it right. That's from 2008 but I suspect that at least for ext file systems, not much has changed, though I don't know that for certain.