I've had it 6 times in 5 months, you absolutely do NOT need to stop bf. Most mastitis is non-infectious anyway and is caused by a back up of milk that your body then attacks. You are then at risk from an infection in this milk. So as others have said, feed, feed and feed.
Make sure you feed in different positions. 'Dangle' feeding can help, where you lie the baby down and dangle boob over them to feed. This way gravity helps drain the affected area. You can also point the chin towards the area since milk is drained most in this region (at least it might be, some evidence seems to show this may not alway hold, but worth a go).
Avoid anything pressing agaisnt your boob, maybe go bra-less if poss until it has cleared. Massage and heat help move milk as well. If after 24 hours it has not gone or got worse, then you may need antibiotics. Even if this is the case they should be safe when bf. There's no reason to consider stopping.
Longer term, think about if there is anyting that could be causing the mastitis - do you sleep with anything pressing boob, wear underwired bras etc, all these things can cause it. Continue feeding in different positions to drain the breast. After 3 months or so your milk production calms down and you may find you dont get it again. HTH.