This was a major infrastructure project of Mr Rajapaksa during his presidency with loan support coming from China.
Namal Rajapaksa and six others were summoned by the Hambantota police last night to record a statement over the protest, police said. They have been accused damaging public property and defying a court order not to protest in Hambantota judicial area.
They were produced before the Hambantota magistrate and ordered to be remanded until October 16 at Tangalle remand prison, the police added.
"We recorded statements from organisers and taken those responsible into custody," a police spokesman said. The number of people arrested since Friday last week over the protest has risen to 40.
The opposition said they are against the sale of assets by the government to foreign entities. Namal Rajapaksa on Monday during a debate in parliament on the airport deal said the government was making Sri Lanka a "playground" for international power games. He was referring to China being given to handle operations of Hambantota sea port and an Indian company being given of operations of the airport.
Both the port and the airport at Hambantota were major infrastructure projects of former President Rajapaksa in his home constituency with commercial loans from China.