Due to travel restrictions and mandatory 14-day quarantines on people coming into the country from Italy, all MotoGP activities in Qatar scheduled for next weekend (7-8 March) have been cancelled.
Moto2 and Moto3 personnel were already in the country doing testing and will therefore race as scheduled.
No word yet on whether World Superbike racing the following weekend will be cancelled.
UPDATE 2 MAR 2020: Thailand Grand Prix on 22 March postponed due to new restrictions enacted by the government.
MotoGP press release for Qatar