"Matches originally scheduled to take place during the international window of 23-31 March 2020 are postponed to later dates," FIFA revealed.
The decision follows a request from CONMEBOL, South American football's governing body, to FIFA on Wednesday, to restage the matches at a later date.
The CONMEBOL letter said it expressed the position of its 10 members: Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Paraguay, Peru, Uruguay and Venezuela.
Many of the South American players selected for their national sides play in Europe, where the deadly disease is rapidly spreading.
FIFA's statement added that it would "continue to assess the situation in relation to COVID-19".
It said it would decide whether further changes to the schedule of South American World Cup 2022 qualifiers were required "always with the aim of protecting the health and safety of all individuals involved".
The fate of the Copa America meanwhile is unclear.
The June 12-July 12 competition is due to be staged in Argentina and Colombia between the South American national sides with also invited Australia and 2022 World Cup hosts Qatar.