The church, The Faith of Christ Evangelical Church, at Igi Olugbin Street, was said to be constituting danger to the people of the area.
The government also ordered that another church under construction and a bar and restaurant built on a canal setback in Shomolu should be demolished.
He gave the directive as he undertook a second-day tour of flood affected areas in parts of the state as a result of last Sunday's heavy rain.
He declared that his government would identify and remove all obstructions to drainage channels in the state.
Fashola, who also inspected drainage systems in Gbagada, Somolu, Iganmu and parts of Surulere, said he would no longer tolerate construction and any other human intervention on established drainage and flood channels.
He said, "The channels are there and they are working. But the places that we have these flood mishaps are largely due to human intervention and obstruction of the channels either by building on them or by blocking them with refuse or other items of such nature.
"When nature takes its course as a result of human action, people's lives are disturbed and it leads to anguish, but we are the cause. This is the time we must stop people from playing games and putting other people's lives at risk."
Fashola urged contractors working on the different drainage systems across the State to reestablish the canal lines so that there would be free flow of water during the rains. He added that there was a need for more dredging of the waterways in order to make them deeper and increase their capacity to hold water.
He lamented that after building more canals, people obstructed the connecting channels resulting in restriction to the free flow of water during the rains.
He pointed to the church under construction and the bar and restaurant at Somolu as examples.
"They have to go too because they are on the canal setback where, ordinarily our machines should take position to work. People cannot build there; it is unacceptable," he said.
The governor said there was little anyone could do about Sunday's downpour which lasted about 16 hours. He pointed out that it had its equalising effect on the ecosystem.
"Without that rain coming down, I believe air travel would have become increasingly difficult. There were thick pockets of cloud in the air, well over 12 to 15, 000 feet which should not be," he observed.
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