The fire began this afternoon. Witnesses said local civil defense fire crews were fighting the blaze.
Authorities could not be immediately reached for comment in Sharjah. It was not immediately clear if there were any casualties.
Fires have affected several skyscrapers in the Emirates, including a February blaze that broke out at Dubai's 86-story Torch tower, one of the world's tallest residential towers. There were no major casualties in that fire.