Fellaini lost his temper after an hour of Saturday's 1-1 Premier League draw between the two clubs and knocked Shawcross to the ground with a swift movement of his head.
The incident went unpunished by referee Mark Halsey but Fellaini can expect a Football Association charge of violent conduct if Halsey confirms that he did not see the headbutt happen at the time.
Everton manager David Moyes condemned Fellaini's actions after the game at the Britannia Stadium and now the Belgium international has made a public show of contrition.
"I apologise completely to Ryan Shawcross, my team mates and to our fans at the game," said Fellaini.
"There was a lot of pushing and pulling going on inside the Stoke penalty area and I didn't feel I was getting any protection from the officials.
"Nevertheless I know I shouldn't have done what I did.
"I have also apologised to the manager and the staff. I have no excuses, I was disappointed with the way I was being treated and I lost my temper, which was unprofessional of me."
Fellaini has scored eight goals for Everton in the Premier League this season.