Holden was forced to pull out of the show's auditions in Blackpool last Sunday (January 22) so that an emergency caesarean could be performed in hospital.
The actress gave birth to daughter Hollie the following day (January 23), but found herself "fighting for life" after she began bleeding heavily and is still recovering in hospital.
Asked during an interview with the Britain's Got Talent website whether she had spoken to Holden, Dixon replied: "I've sent her a message of support and I wish her a speedy recovery.
"I love Amanda to bits - I'm missing my partner in crime and can't wait for her to come back."
Dixon insisted that she had still been able to hold her own against Simon Cowell and David Walliams in Holden's absence, even raising her voice to the pair when they all travelled to Wales this weekend to meet more hopefuls.
"Last night, I shouted at [Simon] and David during auditions in Cardiff," she teased. "I told them to 'Shut up!' They wouldn't let me get a word in edgeways."
It has been claimed that Holden will be temporarily replaced by guest judges for the London auditions next month.
Myleene Klass and EastEnders actress Samantha Womack have apparently been shortlisted for the role.
> Britain's Got Talent Amanda Holden, Alesha Dixon: 'We won't be at war'
Watch Britain's Got Talent stars David Walliams and Michael McIntyre congratulate Amanda Holden below: