Balls, who was partnered with Katya Jones in the 2016 series, has also said the professional dancer made a "big mistake" in kissing her current dance partner, Seann Walsh.
Jones, who is married to fellow Strictly dancer Neil Jones, and comedian Walsh, who was in a relationship at the time, were pictured kissing during a night out two weeks ago.
The former shadow chancellor and Morley and Outwood MP took part in the show two years ago.
He told ITV's Lorraine: "There is definitely a Strictly curse, year after year.
"Luckily there's an age cut-off and I was well above the age."
The 51-year-old said his wife, Yvette Cooper, found the notion of him having a romance with Jones unlikely, adding: "When she was asked about it, she would say 'In his dreams'."
Balls said Walsh and Jones have "had a very tough time the last few weeks", adding: "Katya made a big mistake.
"Neil and Katya are good friends of ours, all they can do is come back and keep dancing."
-> Strictly's Seann and Katya return to the dance floor after kiss shame <- Balls and Jones, 29, made it to the 10th week in Strictly in 2016, and last year she won the show with actor Joe McFadden.
She and Walsh, 32, have faced scrutiny from some viewers over their kiss, but returned to face the music the week after the pictures were printed in the Sun newspaper.