Yes—if the actual front element is broken, a manufacturer or qualified service center can often replace it, but cost and parts availability depend on the exact lens and its age. For a current or recently discontinued Canon L lens, repair is more likely to be practical than for an older model.

In your specific case, the community strongly suggests the lens element was probably not shattered at all; the broken part was likely the UV/protective filter. The clues were the tiny glass shards and the visible front markings, which are printed on the outside of the lens. A real front element is much thicker and would usually break into larger pieces.

If only the filter broke, the lens itself may be fine. Don’t rub loose shards across the glass. Have it inspected/cleaned if glass may have entered the barrel, especially if the filter ring came apart or jammed into the lens. If the element was replaced properly, image quality should return to normal; if only the filter broke, removing it and cleaning the lens should restore normal use.