The 13th season of the marquee T20 tournament, was originally scheduled to begin on March 29.
Finch, Warner and Labuschagne struck fifties to give Australia a fighting total.
England Test series in Sri Lanka postponed due to coronavirus.
The first match of the T20I series between India and South Africa had also been rained off, at the same venue.
Before home series Bangladesh will travel to Ireland on May 8 to play three ODIs and four T20Is.
BCB has postponed the two international T20 matches between Asia XI and World XI in light of the current COVID-19 outbreak.
Liton Das heroics help Tigers outclass visitors in second T20I to complete clean sweep.
A stunning last over blitz from Rashid Khan tied the game, before Joshua Little bowled a top Super Over conceding only 8 runs
Soumya Sarkar fires Bangladesh to thumping win against Zimbabwe
Rohit Sharma, who sustained a calf injury last month, does not feature in the squad.
Alyssa Healy, Beth Mooney, Schutt and Jess Jonassen hand clinical Australia fifth T20 World Cup title.
South Africa beat Australia by six wickets in the third and final one-day international at Senwes Park on Saturday.
Andre Russell shine as West Indies defeated Sri Lanka by seven-wickets in the second T20I at Pallekele on Friday.
Opener Liton Das hit a national record 176 runs as Bangladesh beat Zimbabwe by 123 runs and swept the three-match ODI series on Friday.
Afghanistan were 11 runs ahead on DLS when rain stopped play 15 overs into their chase of 173, giving them a 1-0 lead.
Mushfiqur Rahim has returned to Bangladesh T20I squad, the Bangladesh Cricket Board (BCB) announced,
Australia defeat South Africa by 5-run (DLS) in semifinal; to face India in final
ICC Women T20 World Cup semi-final abandoned, India advance to the final.
Janneman Malan maiden ton, Lungi Ngidi six-for clinch South African first series win of Boucher era.
Pollard celebrates two landmarks as West Indies cruise against Sri Lanka
Bangladesh survive Donalnd Tiripano assault to seal series.
New Zealand welcome back pace trio for Australia ODI series.
South Africa recall Faf du Plessis and Rassie Van der Dussen for India ODI tour.
Georgia Wareham stars as Australia overcome Ellyse Perry injury to clinch semi-final spot.