Whiley was offered her vaccine in February, while her clinically vulnerable sister was in hospital with the virus.
The Radio 1 DJ's sister Frances, who has learning disabilities, has been released from hospital after testing postive for COVID-19 last week.
She will embark on a triathlon challenge for Sport Relief.
Simon Mayo begins new chapter in broadcast career with new show on Scala Radio
The presented said he told the BBC it was a "mistake" to team him up with Jo Whiley.
Radio presenter Simon Mayo has announced he's leaving Radio 2, and the Drivetime show he hosts with Jo Whiley will come to an end.