Jersey's first case of the Covid-19 disease was confirmed on Tuesday.
Guernsey's first was on Monday.
The second person to have tested positive returned to Jersey from north-west Italy on Sunday 8 March. The individual concerned, who has not been identified, immediately self-isolated at home and remains well.
The Government of Jersey says that the person has had no contact with anyone in Jersey since their return, apart from a family member, who is also self-isolating. Both will remain in self-isolation for the appropriate period of time.
Dr Ivan Muscat, Jersey’s Deputy Medical Officer of Health, said: 'As with the first case, officers from Environmental Health are in the process of approaching all relevant contacts. If the team do not contact you then there is no need to worry, and you do not need to contact the department or the helpline. We have all the contact details of the people we need to speak to.
'We want to reassure Islanders that the two people who have tested positive for coronavirus in Jersey are receiving all the care and medical attention necessary. We are working with the individuals concerned to trace any relevant close contacts and ensure that they are managed appropriately.'