Neil announced the news on Friday’s edition of Strictly spin-off show It Takes Two, but told host Zoe Ball he would be ready to train again on Monday, should Alex make it through the weekend.
He said: “I won’t be dancing. I’ve tried, but it’s just not ready yet.
“I’ll be fine if I rest it this weekend.”
He added to Alex: “You nail the dance, go through, then I’m ready on Monday morning.”
The former Arsenal player said that it had been a challenging week without her usual partner, as she prepares to dance the American Smooth on Saturday night.
She said: “It has been a strange week to be honest.
“My partner, I’m used to him. It’s really different dancing with someone else.
“I can sit here and moan. Poor Will doesn’t get to dance.”
The Paralympian missed last week’s live show after he fell awkwardly and injured his knee during a rehearsal.
On Wednesday, a “gutted” Will announced he would be bowing out of the competition, explaining: “I’ve loved being part of the show and am so grateful for the phenomenal support we have received.
“I want to say a special thank you to Janette [Manrara, his professional partner], for believing in me, and giving me the confidence to believe in myself. The things we achieved, from our Couple’s Choice dance, through to our lifts in our Salsa, will stay with me forever. I’ve had the time of my life.”
Strictly Come Dancing airs on Saturday at 7pm on BBC One.