Paul, even a fuzzy cell phone photo would help. It sounds like you are talking about a skeg-hung rudder, meaning the from edge of the rudder is hinged onto something in front of it, another board or the stern of the boat.
Depending on the damage, it is possible to dry wood out and inject epoxy penetrant to stregnthen it, but if the wood is damp and the damage is large you'd probably be safer replacing a critical part--like a rudder mount.
"Marine" materials are best for this, either marine ply (which is particularly dense and solid with no voids) or fiberglass are typical. Aluminum plates would be a bad choice since aluminum easily has galvanic problems in the wet.