Thomas Cook was due to fly a total of 230,000 passengers to Larnaca and Paphos Airports from the UK, Scandinavia and Germany this year, according to sources from airport operator Hermes.
Of these, 185,000 have already travelled.
Thomas Cook represented 4.1% of annual passenger traffic on flights of Thomas Cook UK (2.5% of total passenger traffic), Thomas Cook Scandinavia (1.4%) and Condor (0.2%)
A total of seven flights were cancelled from and to Larnaca to Scandinavian airports on Monday as was a flight from Paphos to Manchester.
The first repatriation flight is to Manchester and is scheduled to leave early on Tuesday morning from Paphos.
There are about 8000 Thomas Cook customers in Cyprus at the moment, of whom 3500 are Britons.