Images show Bishop Charles H Ellis III holding Ariana high above her waist, with his fingers squeezed around the side of the singer's chest.
"It would never be my intention to touch any woman's breast," he told the Associated Press.
"Maybe I crossed the border, maybe I was too friendly or familiar."
He added: "But again, I apologise."
The preacher said he hugged all artists, male or female, during the ceremony commemorating the Queen of Soul.
But viewers began posting images from the service when Ariana got up to sing Aretha's song (You Make Me Feel Like) A Natural Woman. Many people felt that Bishop Ellis's hand was inappropriately high on the 25-year-old's body as he spoke to her - saying that she looked uncomfortable with the contact.
It came as others on social media had been criticising Ariana for what she was wearing to the church service, saying her dress was too short.
Some people said that the focus being on Ariana, rather than the bishop, was misogynistic.
But acts like does not want to be treated like whore. She's attention whore, like all women.
Nolan Perez
This is the state of Weimerica.
A nigger openly fondling the breasts of a goblina on national tv is now acceptable.
Logan Jackson
That's a resting hug. Because of their height difference he'd either have to hug her shoulder which would be weird, or damn near squat/get closer to her to put his hand on her waist, which she's clearly avoiding in that picture.
Parker Wood
That's not just any goblina. That's a goblina whose entire career is training younger goblinas to be whores from a young age.
Luis Long
No minister! That isn't a little boy in your choir class!
