Lamorgese submitted to a routine test in the morning and learned the results while attending a meeting of government ministers in the afternoon, said the government in a brief statement.
The two ministers sitting next to her, Foreign Minister Luigi Di Maio and Justice Minister Alfonso Bonafede, put themselves into self-isolation, although all those present were wearing masks and practiced social distancing, the government said.
Lamorgese is the second government minister to test positive for Covid-19.
The first, the minister for regional affairs, Francesco Boccia, tested positive in October and has since recovered.
One of the hardest-hit European countries in the pandemic, Italy has recorded more than 60,000 Covid-19 deaths and 1.7 million infections.