The Women's World Cup Qualifier was due to take place in Sri Lanka between July 3 and 19, where three teams were to qualify for the 2021 event in New Zealand.
On the other hand, the start of the journey to the U-19 World Cup 2022 was scheduled to begin with the European Regional Qualifier in Denmark between July 24 and 30.
The ICC said that it will work with all participating members to identify when these events will be able to be staged in the future.
"In light of the continuing travel restrictions, global health concerns and government and public health authority advice we have decided to postpone two further upcoming qualifying events due to the COVID-19 pandemic.
The Women's Cricket World Cup Qualifier and the Europe qualifier to the U-19 Cricket World Cup 2022 have both been impacted," said ICC Head of Events, Chris Tetley.
"Our priority during this difficult period is to protect the well-being of players, coaches, officials, fans and the whole cricket community and we will take well-informed, responsible decisions in relation to both postponing events and resuming international cricket."
The global cricket governing body further said it it mointoring the remaining two U-19 World Cup Regional Qualifier Division 2 events and kept under review: the Africa event is due to take place in Tanzania between August 7 and 14 and the Asia event between December 1 and 9 in Thailand. The Division 1 events in all five regions are scheduled to take place in 2021.