Chigvintsev, who partners Australian star Holly Valance on the reality show, is suffering from a back injury.
Brendan Cole, who partnered Lulu but was voted out of Strictly on Sunday, will replace the Russian.
A BBC spokesperson said in a statement: "Artem was initially diagnosed with a transverse process fracture of the lumbar spine.
"However, the latest medical advice from a spinal specialist following further scans is that he is suffering with a combination of joint and soft tissue injury.
"While this medical advice is more encouraging he will still need to rest, so will not be dancing this Saturday. Brendan Cole will partner Holly in this Saturday's show."
'Kiss Kiss' singer Valance commented: "I'm obviously disappointed I won't be dancing with Artem this weekend, but his well-being is very important to me, and Brendan is an awesome guy and we're working hard to bring something new and exciting to this Saturday's show."
Meanwhile, Cole declared:"I'm extremely happy to be asked by Artem to stand in for him this week. It is never nice under the circumstances but I'll do my utmost to help him and Holly out and I'm really excited to have the opportunity to dance with Holly."
They will dance the Rumba to Will Young's 'Leave Right Now' on Strictly, which continues this Saturday at 6.55pm on BBC One.