The Winter Olympics in Beijing in February next year are surrounded by criticism from several quarters.
Both politicians and organizations have criticized the International Olympic Committee (IOC) for organizing the Olympics in a country with a lack of respect for human rights.
The protests in connection with Monday's fire ceremony in Olympia, 250 kilometers west of the Greek capital Athens, were therefore expected.
Prior to the ceremony, four activists, three women and a man were taken into custody.
During the ceremony, three protesters entered the archeological site where the fire was lit.
Two women and a man unfolded a protest banner with the words "No genocide games", held up the Tibetan flag and shouted for a boycott of the games, in connection with the fire being lit.
The ceremony itself, which was attended by, among others, IOC President Thomas Bach and Greek President Katerina Sakellaropoulou was not interrupted
On Sunday, two women were arrested in the Acropolis in Athens after trying to set up a protest banner against the Winter Games, which begin in less than four months.
The Olympics will be inaugurated in 109 days, on February 4, 2022.