Individual treads can be replaced when absolutely necessary. Depending on how the staircase is built, this can be simple or it can be far too complicated for an amateur to tackle. If you can, try to repair the tread without removing it. If this proves impossible, consider your options carefully:

If the treads are “open" on both sides and resting atop the stringers and the handrail balusters aren’t attached to the steps, it might require only pulling up the damaged tread and removing the nails that hold it to the risers above and below it. New, unfinished hardwood treads can be easily cut to fit.

However, if the treads are glued into mortises cut into the stringers on both sides (a "closed" run), or if they are held in place by balusters mortised into each step, removing a single tread could entail disassembling (and possibly destroying) much of the staircase in the process. Before you attempt this work, get an estimate from a professional with proven experience in stair building and repair.