This depends on a number of factors such as how close you are to a stream, river, drainage area, road, or culvert and how badly your property burned. If all the vegetation was removed by a burn and you are uphill from an area of concern (such as an undersized culvert), then yes, water running off your property could be a problem.
The amount of damage will depend on the amount of water running off your property. Small, steady amounts of rain can result in rill or gully erosion, whereas a major storm event could result in more serious problems such as mass wasting, debris flows, flooding, and washed-out roads.
If you are in doubt, it is best to play it safe and contact a professional at your local Natural Resources Conservation Service office.
