Kirkwood had just let Andretti Global team-mate Herta through at Turn 3 when he got into a wheel-banging moment with AJ Foyt Racing’s Ferrucci at Turn 5.
Kirkwood said over the radio: “Santino needs to get kicked out of the series.”
A lap after that, Ferrucci weaved and balked Herta in the Turns 6-7 complex before Herta was able to pull off an inside pass in Turn 8 as Ferrucci dove to pitlane.
The end of the session saw Ferrucci and Kirkwood have a briefly physical exchange on pitlane, with the former claiming Kirkwood turned into him following an on-track altercation.
Ferrucci was seen shoving Kirkwood, with the NBC Peacock audio picking up Ferrucci saying, “You f****** piece of s***, you turned into me!”
Kirkwood stopped attempting to talk to Ferrucci, walking off and smiling back to his timing stand.
“We're in practice,” Ferrucci told NBC. “I'm on a lap that's gonna put us P3, right? I know everybody's fighting traffic.
“I'm coming down the hill and who just turns into somebody and slides the car into you? I mean, it's such a dickish move, man.
“I grew up karting with him, known him a long time. Never seen him do something like that.
“You saw him turn into [Josef] Newgarden yesterday [although Newgarden admitted he was at fault for their light collision]. It's a shame.”
When challenged by the reporter that Kirkwood felt it was Ferrucci who turned into him, rather than the other way around, he replied: “Well, if you go back and watch and you see him step on it and turn left.
“I mean, I don't know what more evidence you need from that, man. He's got the onboard camera, not us.
“So, and then his little boyfriend team-mate over there did the same thing. So yeah, leave it to them, man. We're out here doing our own thing.
“You know, it's Detroit, I'm having a blast. Crew’s all fired up. We know we got a hot rod.”
Kirkwood said the on-track altercation was a result of Ferrucci’s impatience, and that he went to confront him after the session to “tell him that was completely unnecessary”.
“Everyone stops here, right?” Kirkwood said. “Like everyone has to wait, get your gap, get a clean lap in. It's practice, relax – and that's not what he did.
“And he decided to do it to me, then he did it to Colton too. They nearly collided. I don't know what he's doing.
“His lap was already ruined. He just ruined his next lap too. It's just dumb. It's dangerous.
“He drove right into me purposely, tried to drive me into the wall, and then I went up and tried to talk to him about it and then he grabs me. He's like shaking me.
“I’m like, what are you getting mad at me for? It's insane. But we've seen it before with him.”
Ferrucci has recently feuded with Juncos Hollinger driver Romain Grosjean, with the two having multiple run-ins leading up to the Indianapolis 500.
Kirkwood's team-mate Herta, who was fastest in the session, said he didn’t know what he did to make Ferrucci so mad at him either.
“I don't even know what I did,” he laughed. “I don't know, that guy's a head case but I'm happy with our programme. I'm not really sure what I did to make him mad.
“He passed me before the alternate line [where lap timing starts and ends], like we're all waiting for our gaps, and he passed me and so I passed him back and ruined his lap.
“Yeah, he can do his thing, we'll do ours. He's driving a Penske car to P20th again for the fifth consecutive weekend.
“I'm happy with what we're doing here. We don't have time for him and his shenanigans at the back.”
IndyCar will be taking no action over the incident, series officials confirmed to Autosport.