Richardson featured in one match for RCB, returning figures of 1 for 29 in three overs against Rajasthan Royals in Mumbai, but Zampa couldn't make it to the playing XI this season despite the spin-friendly conditions at Chepauk.
The leg-spinner missed the first game of RCB's season because of his marriage.
Glenn Maxwell, Dan Christian and Daniel Sams -- the three other Australian players in the RCB -- will remain at the franchise along with their coach Simon Katich. The event is being conducted in a bio-bubble in front of empty stands.
Sams had tested positive for the virus before the tournament began but has since recovered.
RCB are currently placed third in the points table with four wins from five matches.
As many as 14 Australian players now remain in the IPL, including stars such as Steve Smith, David Warner and Pat Cummins, as well as coaches Ricky Ponting and Katich.
Commentators Matthew Hayden, Brett Lee, Michael Slater and Lisa Sthalekar are also among the Australians involved with the league right now.