Can low levels of iron cause body aches?

Possibly. Iron deficiency can cause weakness and fatigue, which can feel like body aches. Other symptoms can be pale skin, dizziness, decreased exercise tolerance and irritability. If you think this describes how you're feeling you can see your physician and they will run blood work to check for you.
Yes. Low iron levels can be a component of anemia as well as many other ailments....Of which body aches can be associated.