The first problem with things in space is that everything moves fast - REALLY fast. For example, when you're near a planet, it's not that gravity is just too weak to pull you in - it's that you're going really fast and are counteracting gravity. To put a number to it, the international space station is traveling at 17,000 MPH.
With today's bi-propellant technology, if your shield were in the ISS's orbit and 90% of it was fuel and a missile was coming in behind you, the best you could do is go roughly 6,000 MPH in the other direction. However, you wouldn't actually go 6,000 MPH in the other direction: you would instead start falling back to Earth irritatingly quickly.
Changing orbits with today's technology is very difficult.
Furthermore, missiles flying in space are limited in what they can do because they have to carry all their fuel with them and accelerate it as well. This is why ballistic missiles are just ballistic: it's hard to affect changes in your trajectory when you would also have to carry fuel... so they just don't carry fuel and fly. We then lob little things at them to get in their way (EKV: Exoatmospheric Kill Vehicle, which is literally a thing that gets in the way of incoming missiles and runs into them - sound familiar?). These are incredibly expensive and rely heavily on the other target being predictable (in this case, ballistic) so they can minimize fuel usage and cost.
But you asked about the future...
Why did I say everything above? Because, in the future, if you have interplanetary travel, you must have solved the engine inefficiency problem and made it trivial to produce engines that can just do whatever you want. 199
However, your space ships still have structural issues, so they can only maneuver so quickly (unless, I suppose, the entire hull is lined with small engines so it can perfectly distribute forces). Presumably they may have also created some sort of an inertial damper to let them maneuver more quickly.
So let's say the enemy missiles and you both have the technology to make everything maneuver exactly how you want: you still lose because you're still playing defense and defense is always reactionary. If you get your shield right in the way of the missile (because your technology lets you do this effectively), then their missile would just change its course (because their technology also lets them do that). So you figure out how their algorithm works and make your shield predict theirs, so they change theirs. (Note: this is exactly how defense works nowadays too).
Regardless of your level of technology between now and then, you CAN put a shield (whether it be something already in space or something like EKV) between you and them, but you always have a disadvantage that they will have the same maneuverability abilities and they control the game (again, defense is always reactionary). Plus your [big metallic] shield tends to get destroyed when it gets hit. Plus yours has to be a lot more expensive because it has to be more capable than theirs, so they can always exhaust your resources by just firing lots of them at you.
A shield like that really isn't any more effective than shooting their missile with your missile - except that your missile doesn't have to happen to be in the right spot [as much] as a shield does.
This, by the way, is the genesis of energy weapons.
Some more related examples
Using some numbers from wikipedia...
The US's "Minuteman" ballistic missiles cost $7 Million and [technically] only take a few people to operate them from a single silo.
The US's EKV program is hard to estimate the cost of, but [1] says they cost about $90+ Million each. It costs more than 10 times as much to defend against a single ICBM as it does to launch one. But this isn't the whole story, because to be able to hit a flying thing, you first have to detect the flying thing (with radars, which have limited range and precision) and transmit that information (which can be jammed) and launch against it, so you have the cost of all of those pieces too.
This cost differential has always been and probably always will be so.
[1] - http://mostlymissiledefense.com/2012/07/24/ballistic-missile-defense-how-much-does-a-gbi-interceptor-cost-july-24-2012/ 898