This one comes up quite a lot, but often the reason isn't what you might initially think. So, the first thing to check is - what's the source of the problem? Your file? Your code? Your environment? Or Apache POI?
(If you're here, you probably think it's Apache POI. However, it often isn't! A moderate laptop, with a decent but not excessive heap size, from a standing start, can normally read or write a file with 100 columns and 100,000 rows in under a couple of seconds, including the time to start the JVM).
Apache POI ships with a few programs and a few example programs, which can be used to do some basic performance checks. For testing file generation, the class to use is in the examples package, SSPerformanceTest. Run SSPerformanceTest with arguments of the writing type (HSSF, XSSF or SXSSF), the number rows, the number of columns, and if the file should be saved. If you can't run that with 50,000 rows and 50 columns in HSSF and SXSSF in under 3 seconds, and XSSF in under 10 seconds (and ideally all 3 in less than that!), then the problem is with your environment.
Next, use the example program ToCSV to try reading the a file in with HSSF or XSSF. Related is XLSX2CSV, which uses SAX parsing for .xlsx. Run this against both your problem file, and a simple one generated by SSPerformanceTest of the same size. If this is slow, then there could be an Apache POI problem with how the file is being processed (POI makes some assumptions that might not always be right on all files). If these tests are fast, then any performance problems are in your code!