The unfortunate bottom line here is that she's interpreting your behavior as uncomfortable and directed toward her. I agree with the other posters as far as making a point to sit away from her. From there, you have two ways to go:
1) You should make it a point to apologize, in person, and in a reasonably public area (e.g. not alone in the break room, but maybe out near the water cooler) and let her know that you've thought about what she had to say, and you'll do your best not to repeat the behavior. It would probably also be a good idea to casually bring up your concern with your supervisor the next time he/she asks how you're doing. -OR-
2) Discuss the incident with your supervisor first. Some women are sadly inclined to over-dramatize their interactions with men in the workplace (and in life). She may have a history of doing this that your supervisor can help with. It's also possible that for some reason, you just hit her "creepy" meter, in which case there isn't much you can do to fix it except not interact with her to whatever extent is possible in your team environment. Your supervisor needs to be the mediator in this situation, because it has the potential to affect the working capacity of the team. In this case, you could ask your supervisor to sit in on a conversation in which you apologize as above.
I'm not suggesting you've done anything wrong, here, but in my experience women are much more likely than men to report s-xual harassment to their superiors. You don't want to sit through an investigation if you don't have to - even if you're found blameless in the situation, it will follow you around the company in your personnel file, waiting to be looked at every time you get a review or are being considered for a promotion.
Here's another important part: Get yourself a notebook, and write down the original conversation, with a date if you remember it. Write down your apology, and anything she had to say as a response, with a date. Write down your conversation with your supervisor, with a date. Just the facts as you saw/experienced them, not any judgments or opinions. Keep this notebook with you in your personal bag or a locked drawer (as opposed to in a publicly accessible area of your desk).