The former pop group is preparing for a world reunion tour, set to begin Sunday in Vancouver, British Columbia.
Affected by the itchy illness are 18-month-old Bluebell, Halliwell's daughter; and Beckham's 2-year-old son, Cruz.
"Bluebell caught chicken pox from Cruz," Halliwell told "GMTV," according to People.com. "She's completely pelted now, so I left her at home. Normally they're running around the set."
Halliwell added on the official Spice Girls' blog that it was inevitable the illness would spread from one kid to the other since Bluebell "loves hanging with the Beckham boys."
"Cruz and Bluebell have play dates, and Romeo -- well, he is just gorgeous with her," Halliwell said. "Actually, it was a beautiful moment when we were rehearsing the other day and all of our kids were playing on the stage at the same time. It made me smile."
The Spice Girls have a combined seven children.