Leicester have complained to the Football Association about "abuse, provocation and intimidation" they say their players, fans and staff suffered during Saturday's match at Millwall.
The Foxes say they received "numerous complaints" and "will not accept the safety of our supporters, players, and staff being compromised".
Lions fans ran on the pitch after the League One side's 1-0 FA Cup victory.
Millwall said they were "disappointed" the complaint was not made on Saturday.
Mounted police were deployed after the game to keep the home fans away from the Leicester enclosure.
The FA says it intends to speak with the Premier League champions over the issue.
A Leicester City spokesman said: "We have personally congratulated Millwall on a merited victory and wish them every success in the sixth round.
"However, following receipt of numerous complaints relating to the constant abuse, provocation and intimidation of our players, staff and supporters from our arrival at the stadium, throughout the match and in its immediate aftermath, we have registered our dissatisfaction with the FA. We are awaiting their response."
A Millwall spokesman said: "We have been made aware of these allegations today and are extremely disappointed that Leicester City, as is the professional protocol in such instances, did not raise them on the day of the game itself.
"This morning we received an email from Leicester thanking Millwall Football Club for the hospitality extended to them so are surprised that these serious allegations, which should have been discussed on the day, have come to our attention in the manner they have."