If I get mono, how long will my spleen stay swollen?

Duration of illness. The fact that one's spleen swells during the course of mononucleosis means that the spleen is functioning properly. It is a filter for bacteria and abnormal blood cells, and as such will swell in a state that gives rise to these conditions. The spleen size is often monitored by your doctor while you are ill and the recession of spleen size is an indication of improving health.
6-10 weeks. It stays swollen, and is in danger of having rupture or other issues for up to three months.