Do I need to close a ByteArrayInputStream?

You don't have to close ByteArrayInputStream, the moment it is not referenced by any variable, garbage collector will release the stream and somebytes (of course assuming they aren't referenced somewhere else).

However it is always a good practice to close every stream, in fact, maybe the implementation creating the stream will change in the future and instead of raw bytes you'll be reading file? Also static code analyzing tools like PMD or FindBugs (see comments) will most likely complain.

If you are bored with closing the stream and being forced to handle impossible IOException, you might use IOUtils:

IOUtils.closeQuietly(stream);

It is always good practice to close your readers. However not closing a ByteArrayInputStream does not have as heavy of a potential negative effect because you are not accessing a file, just a byte array in memory.

As @TomaszNurkiewicz mentioned it's always good to close the opened stream. Another good way to let it do the try block itself. Use try with resource like.......

try ( InputStream inputStream = new ByteArrayInputStream(bytes); Workbook workBook = new XSSFWorkbook(inputStream)) { 

here Workbook and InputStream both implements Closeable Interface so once try block completes ( normally or abruptly), stream will be closed for sure.

Resources need to be closed in a finally (or equivalent). But where you just have some bytes, no it doesn't matter. Although when writing, be careful to flush in the happy case.