Yes, you can install a box, preferable a metal box, to protect the electric panel.
Be sure the box has a door (or two doors) to make it "accessible". Nothing must be put at less of three feet from the front of the new box.
I don't know where you live at, but the electric meter must be left outside the box. You actually won't need to remove any cable, just to cut on the top of the box an entrance in the area where the cable between the meter and box is located, in order to install it close and flat to the wall. There is not need to install a back panel in the box, you just seal the surroundings of the new box to the wall of the house with caulking. The new box, however, must be bolted and secured enough to the wall.
After that, you put some sealer paste, usually of grey color around the entrance cable, and this sealer paste can be bought at any electric store, I think that Home Depot sells it as well.
Having the new box its own door, you might won't need a door in your current panel, but you can keep it, it will make your electric panel more safe, in case the door of the new cover box is left open by any chance.
The point is to make the electric panel accessible, this is to say, with enough space to turn breakers On and Off, to remove the breaker panel front frame and make repairs inside of it.
Again, you might don't need to change the electric meter, neither the electric panel. Just install a box, leave the meter outside over the new box, and you are good to go.