The world championship rivals both retired following contact at the first chicane midway through the race, while battling over ninth position.
Slow stops for both drivers had seen them lose ground to the front of the race, Hamilton rejoining behind Lando Norris in an effective fourth (others ahead were still to stop).
As he rejoined, a recovering Verstappen drew alongside, taking the outside line into the first chicane before the resultant contact on the apex of the second corner.
“We were racing for position today but you need two people to work together to make the corner and Lewis just kept squeezing until there wasn't room any more for two cars and that's when we crashed,” explained Verstappen.
“When he exited the pits, he started to squeeze me going into Turn 1 so I had to use the green part of the track.
“It was very tight but there was room for me to go around the outside and then I was pushed onto the orange sausage kerb.
“I was there to try and race hard but fair,” he added.
“I don't fully agree with the penalty as I believe it was a racing incident.
“It's very unfortunate what happened today but we are both professionals and so we will move on.”
Following the crash, Verstappen quickly climbed from his car and left the scene of the incident, while Hamilton attempted to free his Mercedes and rejoin the race.
Ultimately, the Englishman too was forced to abandon the race, his car heavily damaged and he later credited the halo with saving his life.
It's the latest clash in the duo's world championship battle, having previously made contact at the British Grand Prix.
In that instance, Verstappen was fired into the barriers on the opening lap when Hamilton nudged his right-rear wheel at Copse.
The Englishman received an in-race time penalty for his role in the incident which saw the Red Bull driver taken to hospital.
That crash all but guaranteed the need for Verstappen to take an additional power unit in the latter stages of the 2021 season.
With a three-place grid penalty for Sochi next time out, it's expected the new Honda will be taken that weekend.
“We are disappointed with the three-place grid penalty, but accept the stewards decision,” said Red Bull team principal, Christian Horner.
“We felt what happened between Max and Lewis was a genuine racing incident.
“You can argue for both sides but ultimately it's frustrating and disappointing to see both cars out of the race in what is proving to be an exciting championship.
“The main thing today is that the halo ultimately did its job and certainly this isn't the way we intended to finish the race.”
Sergio Perez in the second Red Bull crossed the line in Monza third, though was classified fifth after a five-second time penalty was applied.
Perez was soon after caught by Valtteri Bottas, who subsequently shadowed the Red Bull to the flag, unable to pass but ultimately awarded third place.
“It was a very eventful race and a real shame to miss out on the podium,” Perez said.
“With the penalty, I think we hoped for a wider view in the sense that it was my corner and I was ahead of Charles, but it is what it is and we tried to recover.
“From our side we did the best possible race we could as a team but overtaking was impossible today and it was really difficult to keep ahead of the cars behind.”
Verstappen continues to lead the world championship by five points over Hamilton, while Red Bull has lost further ground to Mercedes in the constructors' battle to now sit 18 points in arrears.
Formula 1 heads to Sochi for Round 15 of the season on September 24-26.