"It has been really stressful and really hard times over the past few weeks and we are still going to be here for a little while until he [his son] is ready to take home. I've got to pay to see my son," Dexter said.
He told Fairfax it was unfair on nurses and relatives of patients.
His petition has a target of 100,000 and has so far gained more than 9000 signatures.
A Wilson Parking spokesman said the company managed car parks for two DHBs - Auckland and MidCentral.
An Auckland DHB spokesman said the Government told hospitals 15 years ago to sell their car parks, so Auckland City Hospital's was sold to AMP Capital and was managed by Wilson.
There was revenue return to the DHB from the car park but the spokesman would not comment further.
A Counties Manukau spokeswoman said the Middlemore Hospital car park was managed by a company called Secure Parking.
"We make no money from parking which is managed by Secure Parking Ltd. Further, we can sometimes offer 'compassionate' parking for people who need it. People need to see the charge nurse of the ward they are visiting," she said.
The company has been contacted for comment.