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Gravitational field produced by a mass is always in the same direction(towards the mass) while in case of electric(electrostatic) fields two different kinds of electric charges produce fields in opposite directions. Also any two gravitating masses always attract each other; whereas in case of electric charges, they may attract if they are of the opposite sign or repel each other otherwise. It is precisely this duality of charges and their relation with each other that makes electric shielding by a conductor possible.

However if there were an ambient gravitational field, whatever movable masses are there in the region concerned will move in the direction of the field but the gravitational field produced by them will aid the ambient gravitational field rather than oppose the ambient gravitational field. This will change the net field in the conductor thus leaving no possibility of shielding.