The passengers on the Jet2 flight from East Midlands Airport were warned to cover up the slogan on the back of their tops - which read "b------ on tour" - but they refused to do so.
Police were called to the incident but no arrests were made.
A Jet2.com spokesman said: "At check-in for our East Midlands to Majorca flight this morning, a group of passengers were reminded of our Onboard Together policy and told that they would not be permitted to fly with us whilst wearing t-shirts which displayed offensive language.
"The group were asked to either wear different attire or cover up the offensive language, and were reminded of this on numerous occasions, including by the airport police whilst in the departures area.
"Once in the cabin, and in the presence of families and young children, several members of the group decided to ignore these repeated warnings, at which point our crew took the decision to remove them from the flight."
"The flight has departed, and we apologise to all other customers for the delay and inconvenience that this caused at the start of their holiday.
The Leicester group were flying from East Midlands Airport to Mallorcahttps://t.co/vyrpY9X0HN— Leicester Mercury (@Leicester_Merc) 30 May 2017
"However, as a family friendly airline that carries millions of holidaymakers, including families with young children, we will not allow people on board if they are using or displaying offensive language, or if they fail to comply with the instructions of our crew."
Leicestershire police confirmed that they attended the incident but the matter was dealt with by the airline and no arrests were made.
One member of the party said the bride-to-be was "devastated" and all the group had to book new flights from different airports around the country.