Hair algae (which is what it look like in the pic) can quickly spread through a tank and is a pain to get rid off. Depending on your water parameters it may / may not spread (most importantly your phosphate levels - if you haved detectable phosphate, it will spread).
I would suggest taking the rock out of your tank, and scrubbing it with a stiff tooth brush or wire brush to get the hair algae off it. Put it back in your tank, then repeat as necessary. Just make sure you scrub the rock outside of your tank, or else you will release algae spores into your tank...then the algae will surely spread.
HTH,
Stewart
ps - it may take people some time to answer a question, often far longer than the 45 minutes you left your message up for before bumping it - generally if someone has not replied in day, then you should bump it up (unless of course it is an emergency of some sort). A little patience is important - mostly in reef keeping.