Beccy is the show's current assistant producer.
Speaking live on air during this afternoon's (January 14) BBC show, Mills said: "Really sad news. This Friday is going to be Beccy's last show with us. It's going to be weird."
Earlier today, Mills tweeted: "If you're a fan of my show you NEED to listen today @BBCR1 from 1pm. An important announcement and I wouldn't want you to miss it"
Explaining further about her departure, Beccy stated: "I haven't been on the show full time for a while. A while ago I got MS (multiple sclerosis) which is rubbish. I stopped walking, being able to rap. I want to come back to work full time but I can't do it.
"I'm not leaving Radio 1, I'm going to go back with (BBC radio producer and 'The Surgery' presenter) Aled."
Talking to Mills, Beccy revealed that it was the show's listeners who initially helped her realise the severity of her condition.
"It was kind of diagnosed by some listeners on Twitter who heard me mention my symptoms and texted in - so thank you for that because I actually went to the doctor."
Mills went on to confirm that Friday's (January 18) show will be his colleague's last: "It is the best thing to do but I am going to miss you. You know there is always a place for you here.
"We've been talking about it for a while but Beccy's last show will be Friday and we're going to make it a good one. We're all really sad about it."