The former Italian defender and his son who plays as a midfielder for the club were both diagnosed with the disease after experiencing symptoms.
The Serie A club announced that Paolo and Daniel Maldini are both well and have already been in self-isolation for two weeks.
A statement on Milan’s website read: ‘AC Milan confirms that Paolo Maldini, the club’s technical director, became aware of contact with a person who subsequently tested positive for coronavirus and began to display symptoms of the virus himself.
‘He was administered with a swab test yesterday, the result of which was positive. His son Daniel, a forward in AC Milan’s youth team who had previously been training with the first team, also tested positive.
‘Paolo and Daniel are both well and have already completed two weeks at home without contact with others. They will now remain in quarantine until clinically recovered, as per the medical protocols outlined by the health authorities.’