Dixon, the six-time IndyCar champion, had spun on the course and reentered the track ahead of Romain Grosjean and Power. Dixon allowed enough room for Grosjean to get by, but as Power approached, the gap closed and Power couldn't avoid hitting Dixon.
The two cars spun off course and Power slammed into a concrete wall. Both cars were extremely damaged, with only three hours to rebuild them ahead of qualifying.
Power then got out of his car, exchanged words with Dixon and shoved him in the chest. Power later kicked the air in frustration.
"Scott moved abruptly and I was coming," Power said. "It's a very unfortunate incident. Nothing I could really do there. Didn't expect him to move. Such a pity. I felt like we had a pretty good car. We'll rebuild it and see what happens."
Dixon acknowledged he was at fault.
"Didn't realize Power was even there," Dixon said. "I'm really sorry for him and obviously his team. Mistake on my behalf. I feel frustrated for obviously wrecking our car and his car as well."
Power, who will start 22nd in Sunday's race, was still upset later Saturday afternoon -- and his anger wasn't solely directed at Dixon, who ended up using an entirely new car for qualifying and will start 23rd on Sunday.
"Grosjean, he's a piece of crap for what he did in practice," Power said. "He needs a punch in the face."
Power then targeted the Road America course that has undergone its first repaving since 1995.
"This track's terrible when you go off it," Power said after going off course in qualifying. "They do a terrible job here. They need to pick up their game. Any way you go off, you almost break your back every time. I've done it a couple of times this weekend. Need a kick in the butt for this place."
Colton Herta of Andretti Autosport earned the pole position for Sunday's race by posting a fastest lap of 1 minute, 40.1945 seconds on the 14-turn, 4.014-mile road course. That's over 4½ seconds faster than the time Alexander Rossi ran to earn the pole for last year's event.