Ajimobi said Shiitu's behaviour conduct is not befitting of a governor or an aspiring one for that matter.
Shittu had declared his intention to run for governor in the state in 2019 and has accused Ajimobi of being desperate to stop him.
But Ajimobi said he has nothing against the minister. He, however, insisted that Shittu does not have the qualities to be a governor.
Both Ajimobi and Shiitu are members of the All Progressives Congress (APC).
The Governor made the statement while speaking in an interview with Channels Television on Monday, June 18.
"He (Shittu) doesn’t have what it takes to be a governor. I have been a governor now for seven years. I know the qualities of someone who should be a governor; he doesn’t have it. His temperament cannot be that of a governor", Ajimobi said.
According to him, a governor must have some sense of decorum and should have proven his expertise in his chosen field.
"I was an oil and gas man. I rose to the peak of my career as a managing director," he said, stressing that he did not work for just any company but rose through the ranks to become MD of a subsidiary of Shell Petroleum.
"Not only in Nigeria but outside Nigeria. I was chief executive of Shell (Petroleum) companies outside Nigeria," he added.
The governor said he does not have anything personal against Shittu, adding that his stance about the minister's incapability to be a governor is just the facts.
"If you behave unconventionally and I say you behave unconventionally, is that derogatory? I have nothing against him, to be honest. I just like people to have decorum, I like people with style," he said.
When asked if he thought President Muhammadu Buhari would have appointed Shiitu as a minister if he truly lacks leadership qualities, he said the APC in Oyo was against the appointment.
"The party didn’t support the nomination," he said.
However, Ajimobi believes that it would be up to the people of Oyo State to decide who would govern them should Shittu become a governorship candidate after the APC primaries.