It comes as the West Suffolk MP avoided elimination for the sixth time, after radio DJ Chris Moyles was voted off on Thursday’s show.
Speaking on BBC’s Question Time about Hancock’s time in the jungle, Burnham said: “He’s clearly better at showbiz than he is at politics…better at Bushtucker trials than clinical trials, for sure.”
He continued: “He’s not, in my view, a bad person, but it is a bad judgement because politicians should be about we – what’s good for us.
“But this is all about me, isn’t it, me, me and my situation and a cost-of-living crisis for his constituents.
“(There) are things that he should be here answering for, not in the jungle trying to curry favour with other celebrities and the British public.”
Hancock held the post of health secretary during the majority of the coronavirus crisis, during which time the vaccine was developed and tested.
Moyles, 48, told hosts Ant McPartlin and Declan Donnelly he was “gutted” that Hancock was more popular than him after making his exit from the show.
Tory MP and former contestant Nadine Dorries suggested that celebrities who had been “mean” to Hancock were being voted off first.
“Not been the best series to watch as contestants usually far nicer and kinder people.”
Moyles admitted it was difficult for him living alongside the former health secretary in camp, saying: “I really struggled with it, to be fair.
“And then what I did was, because I slagged him a bit, I separated Matt Hancock with Matt because we were living with this guy, and he was doing his best to win us stars for food and everything and chipping in so I had to separate the two.
“Matt Hancock I’ve got major issues with but Matt – less issues.”
In Thursday’s episode, Moyles had questioned Hancock about the inner workings of Westminster and how an MP can move between Cabinet offices without prior experience in the area.
Hancock replied: “The job of the minister is not to be the subject matter expert. Of course, you need to get to grips with the subject matter, but that is only half the job.
“There’s a load of transferable skills: Handling Parliament, communicating with the public, taking decisions effectively, and then you have the subject matter experts who advise you on it all.”
Moyles said: “I’m starting to think now, to be Minister of Transport, all you need is a car. And to be Minister of Health all you need is to be breathing.”
The radio presenter added: “Fascinating talking to him, however, he has no interest in me, my life, my job. He’s a funny little fish, isn’t he?”
Hancock has also faced criticism from across the political divide for joining the reality show at a time when Parliament is sitting.
I’m A Celebrity…Get Me Out Of Here! continues on Friday at 9.15pm on ITV1 and ITV Hub.