Rubiales has been under fire after kissing Hermoso on the lips while handing the women's team their medals after they beat England 1-0 in the final on Sunday.
The incident sparked outrage within and outside Spain, with many, including government ministers, demanding his resignation.
Pressure continued to mount during the week after FIFA opened disciplinary proceedings against Rubiales and Hermoso said in a statement that such acts "should never go unpunished."
As backlash mounted, Rubiales, who initially called his critics "idiots", issued a video apology late on Monday, but it failed to quell the uproar.