The DJ announced the sad news on social media, prompting an influx of support from his followers.
“I hope you enjoyed my @bbcradio2 shows this weekend,” wrote Blackburn on Twitter, “which were recorded before I got the sad news that my lovely sister Jackie had passed away.
“She had been in hospital with Covid and had been home for a week but lost the battle. I love you Jackie R.I.P.”
In a follow-up post, Blackburn confirmed that he will return to the airwaves next week, but he needs “a bit of time to get over my sad news”.
“Thanks for all the lovely messages my friends have sent me it’s very kind of you,” he added.
Jacqueline was Blackburn’s youngest sister, and the presenter has occasionally talked about her in interviews. After contracting polio at an early age, she had been a wheelchair user all her life.
Blackburn hosts multiple regular shows for BBC Radio 2, including Tony Blackburn’s Soul on Sunday, in which he plays a selection of Soul and Motown hits.