The unnamed woman has been transferred to a medical facility and the Women's Six Nations against France scheduled for tonight has been called off.
"I speak for everyone involved in our squad and we send our best wishes to the player”, Hogg said, ahead of the Scotland’s men’s Six Nations match against France in Edinburgh tomorrow.
Hogg, who was named skipper before the competition, said the virus had caused his team to change their daily routine.
"Normally we greet each other every single morning with a handshake but we have stopped that now, we are just bumping elbows,” he added.
Another seven Scotland players and members of the management team are self isolating.
The decision was taken by Six Nations in consultation with Scottish Rugby, the French Rugby Federation (FFR).
The Scotland women's team returned from northern Italy on February 23 after their scheduled match against Italy was postponed.
The country is Europe’s worst-hit by the coronavirus with its death toll reaching 197 to date.
It has been reported 49 deaths occurred in just 24 hours in Italy, according to the BBC.
The number of coronavirus cases in Scotland reached 16 this afternoon after five more people were tested positive, according to the Scottish Government.