Could be a lot of things, but at this time of year the tree should be making lots of new healthy growth.
Is this a small specimen, a fully grown tree, in a pot, or in the soil? My first thought was overwatering, but there are fungal diseases which affect figs. I'd cut off the affected leaf anyway.

Not sure what kind of fig you're talking about, indoor or Ficus carica, the fruiting one grown outside. Brown tips on houseplants usually means underwatering, or very dry air.