All three are family members of a government employee, who was found to have contracted the disease two days ago, said Avijit Roy, the nodal officer for COVID-19 in the UT.
A resident of Bambooflat area in South Andaman, the 49-year-old man had been keeping unwell since April 10.
One of the three people who tested positive on Sunday is the government employee's wife.
They are all undergoing treatment at the GB Pant Hospital here, officials said.
Of the 15 cases reported in the UT, 11 have recovered.
The administration in the islands has adopted the "pool testing" method using less number of kits.
The new method involves testing multiple samples at one go, the officials added. COR SOM RMS RHL