In the footage a woman is seen lying on her back on the grass with her legs parted.
A man, wearing a blue jacket, is on his knees and appears to be using his hands on her.
The video was uploaded to Facebook by a stunned driver who had been making their way through the A63.
It has since led to the arrest of a man, 49, and a woman, 22.
They have been arrested over reports they “committed a sexual act” in Mytongate on Saturday at around 5pm.
In a statement, police said they had been arrested on suspicion of indecent exposure.
They added the duo had been released under investigation.
A statement from police read: "A 49-year-old man and a 22-year-old woman have been arrested on suspicion of indecent exposure following an incident outside William Booth House in Hull on Saturday, August 10.
"They were reported to have committed a sexual act around 5pm.
"They’ve both now been released under investigation."