This is often due to a urinary tract infection. The bacteria causes inflammation in the bladder, which in turn causes bleeding and can be seen as either brown or red depending on how concentrated the urine is.
A urinary tract infection can often easily be treated with a round of antibiotics, but it is not something to put off treating for too long, as it is very uncomfortable for the cat and can eventually lead to either kidney infections or chronic cystitis.
Your vet will want to check a fresh urine sample to determine which type of bacteria is causing this and if crystals or casts are present, then choose the proper antibiotic for curing.
Best of luck, and let me know if I can help further.
You're welcome, and hope this clears up quickly.