The pair, who sit atop the Formula 1 driver's championship standings, were locked wheel to wheel in the 26th lap and with Hamilton looking to squeeze Verstappen of space, the Dutch driver appeared to bounce off a curb on a corner, flying into the air and landing on top of Hamilton's car.
Verstappen could be heard on his team's radio saying: "That's what you get when you don't leave the space."
Both drivers were able to walk away from the incident. The FIA, motorsport's global governing body, announced that the incident would be investigated after the race.
The two drivers had almost come in contact earlier in the race, when they came wheel to wheel in a battle over second position in the opening lap.
"He pushed me wide," seven-time world champion Hamilton said over the radio.
After the race, Hamilton told reporters that he felt "fortunate to be alive."
"I have been racing for a long, long time," he said. "I am so grateful I am still here. I feel incredibly blessed that someone was watching over me today. It is a big shock. We are taking risks and it is only when you experience something like that that you get the real shock of how you look at life and how fragile we all are."
Hamilton added: "I don't think I have ever been hit on the head by a car before. And it is quite a shock for me. If you look at the images, my head is really quite far forward. His rear wheel landed on the halo and the inside part of his tire landed on my head.
"I will need to see a specialist to make sure I am good for the next race because my neck is getting tighter and tighter."
Ahead of the drama, Daniel Ricciardo produced a calm and collected performance to win his first race of the season.
The Australian overtook Verstappen before the first corner of the first lap to come from second place in the grid and led for the majority of the race.
His teammate Lando Norris made it a McLaren 1-2, finishing second ahead of Mercedes driver Valtteri Bottas.
And in celebration, Ricciardo took off his shoe, filled it with champagne and drank it. Even his teammate Norris joined in the "shoey" celebrations.
"To lead, literally, from start to finish, I don't think any of us expected that," he said afterward. "There was something in me on Friday. I knew something was good was going to come.
"For McLaren to be on the podium is good, but a one-two? This is for team papaya."