The Ghanaian 26-year-old was filmed in the dressing room after the final whistle as the players celebrated, with Amartey at one point picking up a Chelsea pennant which was exchanged between the sides before kick-off.
He then proceeded to throw it over his shoulder onto the floor, leading some supporters to criticise him on social media.
Sky Sports News explained on Monday morning that the Foxes had been in touch with the Blues over the incident to calm any tensions, with the pair set to meet again next weekend.
The report said: “Leicester City have apologised to Chelsea after video emerged of Daniel Amartey throwing their pennant on the floor in the wake of their FA Cup victory celebrations.
“Chelsea have accepted the apology and always get on very well with Leicester as a club.”
Amartey has been spoken to about the incident by his club, Sky confirmed.
He did not feature in the final at Wembley, having been named as a substitute and remaining unused by Brendan Rodgers as the Foxes won 1-0.