It looks like just a plastic ceiling box without any extra support. If that is the case, the answer is no, you would definitely want to replace it with a fan box which you can get in kit form. See the picture. You can find these kits at Lowes for under $20. The nice thing is that it looks like you have a single cable coming in which makes the replacement much easier than if you had splices to take apart and try to get wired back together in the new box.
To get the old one out, it will probably take a hammer and screw driver. Bust it out, pry it out, whatever. Be ready for insulation to possibly fall out and make a mess. The new kit has a brace bar with feet on each end that need to be able to sit flat on the top of the ceiling drywall, lath & plaster, or whatever ceiling material you have. The brace bar expands as you twist it to spread across and wedge itself between the ceiling joists. You have to line it up with the center of the hole. Then the box attaches by way of four screws and a little horse-shoe shaped hanger that mounts over the bar. For a fan you should use the #10 screws. This kit I've shown can support up to 110 pounds.