Leicester said it is "deeply concerned" and has launched an investigation after the emergence of a video apparently showing three of its squad in the offensive video.
Defender James Pearson, 22 - the son of the club's manager and former Newcastle coach Nigel - striker Tom Hopper, 21, and goalkeeper Adam Smith, 22, all appear naked in the video, obtained by the Sunday Mirror.
In a statement the club said the players "would like to convey their sincere apologies for their behaviour - to the women involved in the incident, to the club and its owners, to the club's fans and to their families".
Fans and members of the Thai community have called for the trio to be sacked, and the players are flying back to the UK where they will be investigated by the Midlands club.
The video appears to show the three men naked in a hotel room laughing and egging each other on while they make racist and crude remarks as Thai women engage in sex acts.
The club is owned by Thai billionaires and the shocking video was reportedly filmed while players were touring the country celebrating staying up in football's top flight.
It is alleged the trio shared the explicit video with friends back in the UK.
On Sunday, fans told of their disgust on the fans forum FoxesTalk, where one posted: "Get rid of them, never getting near our squad anyway."
Another wrote: "Disgusting and inexcusable behaviour, exactly the sort of stuff that gives British tourists a bad name when we go abroad. It's especially disappointing given the efforts the owners are going to to ensure we're a popular club in Thailand."
The players could face the sack after the club announced it will carry out an investigation into the scandal.
A Leicester City spokesman said: "The Board of Leicester City Football Club is deeply concerned about an incident involving three of our young professionals during a recent trip to Thailand.
"Our players at every level are expected to behave as representatives and ambassadors for our football club, both on official club duty and in their personal lives, so we treat their conduct extremely seriously.
"Following a preliminary meeting in consultation with the three players earlier today, the players involved in the incident are now returning to the UK, in advance of the rest of the squad.
"Tom Hopper, James Pearson and Adam Smith would like to convey their sincere apologies for their behaviour - to the women involved in the incident, to the club and its owners, to the club's fans and to their families.
"A formal process of investigation will be undertaken with the players in conjunction with their representatives and, as such, no further comment can be made at this stage."
He added: "Leicester City remains wholly committed to promoting equality in football and in wider society and to our players recognising their responsibilities as role models to young people."
Piara Powar, the executive director of Football Against Racism in Europe (FARE), accused the stars of being "privileged young men" who are "exerting their power" over women and "demeaning them sexually and racially abusing them".
He added: "There is no point in pretending that videos like this aren't made and shared all the time, but the arrogance of doing it while on a goodwill trip to the country of your owners, the people paying your salaries, is mind blowing.
"The fact that they are Premier League footballers, and one of them is the manager's son, means that there is a responsibility to behave, like it or not.
"I hear Nigel Pearson takes a strong stance against discrimination. It's a shame he hasn't passed the message on to his players and even more of a shame his son doesn't get it."
The scandal is a huge embarrassment for the club, which has campaigned against racism and is owned by a Thai billionaire family who have pumped millions into the club and building its fan base in the Far East.
Nigel Pearson, is a patron of the charity Show Racism the Red Card, which uses the high profile football enjoys to campaign against racism.
The side's Thai owners, father and son Vichai and Aiyawatt Srivaddhanaprabha, will also be angered by the revelations, which could damage the club's close relationship with the country.
Leicester have been in a "strategic, international partnership" with the Tourism Authority of Thailand for three years and the authority's Amazing Thailand branding is on the back of team shirts.