How long does it take for the side effect of brown urine to subside when taking the drug Macrobid for a uti?

Varies. The brownish coloration or the urine is from blood in the urine because your baldder was irritated by an infection, for which you are now on the macrobid. However, it may take just a couple of days for the blood to clear up, or s long as a week if it was really irritated. Also, if the infection went up to yor kidneys, could even be longer. Drink lots of water to flush and make sure to finish meds!