The three new cases are family members of a confirmed case on Monday.
Health bosses have confirmed five Leicestershire residents have now tested positive for Covid-19.
Together with the local NHS, Public Health England and the county council are continuing to work closely together to respond.
Public Health England is currently contacting people who may have had close contact with the three new cases - all three are family members of the case confirmed on Monday (9 March).
Close contacts will be given health advice about symptoms and emergency contact details to use if they become unwell in the 14 days after they had contact with the confirmed case.
Mike Sandys, director of public health for the county council, said: "It's important to reassure people that the risk to the general public remains low.
"We are working closely with colleagues in health to do everything we can to stop the virus spreading and ensure the people of Leicestershire are protected.
"It's a simple step but the best thing people can do is to wash their hands regularly and thoroughly. Good hygiene is the best prevention and this includes washing your hands regularly and thoroughly. If you cough, cover your mouth and nose with a tissue.
"If you have recently been to one of the affected areas and are feeling unwell, you should use the NHS 111 online coronavirus service or call NHS 111 for further advice straight away - please don't go to your doctor or a hospital. There's lots of advice on how people can protect themselves online at www.nhs.uk/coronavirus ."
The first case confirmed in Leicestershire case was announced on Saturday (7 March) and the second on Monday (9 March).
Another separate case at Loughborough University was reported last Saturday but this does not involve a Leicestershire resident.