Great question — answering as the UphillTech team:
The best approach is to wash the shirt. Go into the bathroom, take it off, rinse it throughout, then use hand soap and water on the arm pits and anywhere else you typically sweat enough to make a shirt wet (eg on the back or neck area.) Soap kills the bacteria that were living on the fabric and producing the smell. Rinsing removes the smell molecules they have already produced. Rinse it thoroughly and wring it out well. Then use the hand blower in the bathroom to dry it at least somewhat. It will probably still be damp when you put it back on, but as long as you don't leave wet spots on chairs, people probably won't notice. Disclaimer: this won't work in a place with a more formal dress...
Full answer by Kate Gregory: https://lifehacks.stackexchange.com/a/27703 (CC BY-SA 4.0).
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