In a statement Mr Jack said he has not been tested for the virus but has symptoms including a mild temperature and a cough.
He said: “In the past 24 hours, I have developed mild symptoms associated with coronavirus.
“In line with medical guidance, I am self-isolating and working from home.”
He is the third cabinet minister to go into self isolation this week, after Prime Minister Boris Johnson and Health Secretary Matt Hancock both tested positive for Covid-19.
The UK Government’s chief medical officer Chris Whitty has also gone into self isolation with symptoms.