At first glance this seems like a strange question. How could a disease that has been (so far) mostly contained in one region of the world impact the global monetary system? So long as the disease is contained, it shouldn't. The problem comes when it starts showing up around the world and people began to react in fear.
The Dallas, Texas area has become a focal point for global attention on this topic. Here is an article in the Dallas Morning News that deals with it.
Since we live in this area (the DFW metroplex) we can provide a bit of on the ground report as to how people are reacting to the situation. For the most part people are still calm. There is concern of course and people do watch the news daily for updates. But there is no sign of any panic reaction. For the most part people are carrying on their daily routines. An example might be the State Fair of Texas held annually in Dallas. Despite the fact that millions of people from many different places attend the fair (making it a place one might worry about catching a contagious disease), there has been no drop in attendance this year.
Our family visited this past Saturday (on the day the Texas vs. Oklahoma football game was played). I did not hear a single person talking about Ebola or expressing any concern about it at the fair. The crowd was huge as is typical for this annual event.
The problem might arise if the disease begins to spread and officials cannot explain how it happened. Just this weekend a nurse who attented to the ebola patient who died here in Dallas came down with ebola. So far, there is not an explanation as to how someone who should have been fully protected got the illness. So this will bear watching.
To answer the original question. If the disease starts to spread and people lose confidence that offiicials can contain it, this could start to impact the economy. Obvious places that could get hurt first would be airlines, hotels, restaurants, and any place where the public gathers. But if a real panic took hold, schools could shut down, businesses might have to close etc. We are not near that situation right now in this area.
But you can easily see all this could impact the economy, the financial system, and the monetary system. Even the exchange of paper currency could become suspect since it is a place where germs can circulate.
Right now it seems unlikely, but the answer is yes. Ebola could potentially impact the system. Let's just hope it doesn't.