It can be done, but for some reason they make it very difficult! Place a colored shape underneath your grayscale image, and open the Transparency palette.
Select both the colored shape and the grayscale image, and in the flyout menu on the Transparency pallette, select 'Make Opacity Mask'. Make sure it's set to 'Invert Mask', and that should be the effect you need.
In reality, the image isn't being colored, but is acting as a mask to whatever is underneath. More or less the same effect though, but a little over-complicated!