There are a couple of ways you could tackle that.
If you can do mortice & tenon joinery then make a frame with a groove all round the inside. Make the panel itself out of matching, but paint it before you assemble the door, so that when the matching shrinks, and it will, you are not left with exposed wood.
Another approach would be to use a solid piece of MRMDF for the door. Cut a rectangular hole in it and then rebate that on the back side. You can buy MDF panels with that T&G effect routed into the surface, so just cut a piece to fit and glue it in place.
S