If the aim of hiding eyebrow piercing is to pass a medical test which can not be taken with metal on your body, consider making use of an acrylic retainer. Acrylic retainers are specifically designed for hiding piercing on any part of the body. The acrylic retainer will slide into the eyebrow piercing preventing metal detectors from setting off.
For going to a public place where people with body piercing are not allowed, replace the existing barbell with a barbell which has balls that match the tone of your skin. The metal piece remains intact while the balls hide it from public view by blending into the tone of your skin.
If you do not have too much time and need to hide the eyebrow piercing rather quickly, simply unscrew the balls on the barbell end. The metal piece will be very hard to notice once the balls have been unscrewed. Use this technique if you want to hide the piercing momentarily, probably from a nosy grandma.
Remove the jewellery from your eyebrow. Slide a sterilised piece of fishing line into the piercing. This technique will work best for you if you need to hide the piercing before going to work every day. Simply remove the fishing line and put the jewellery back on when you come back from work.
Consider covering up the piercing with a piece of bandage. This method works best if you need to hide the piercing for a short span of time. Undoubtedly a made-up story will be required explaining the bandage. The safest story would be a bug bite.