The Red Bull driver was caught between the Ferraris of Vettel and Kimi Raikkonen towards the first corner at the Marina Bay Circuit and it resulted in a collision which also saw Fernando Alonso taken out in his McLaren-Honda.
Vettel managed to carry on momentarily, but the damage sustained on Turn 1 proved too much and he was forced to retire.
The German, who started on pole position and was hoping to overhaul Lewis Hamilton's three-point lead at the top of the drivers' standings, is now set to fall well behind the Mercedes' driver in the race for the title.
Vettel claimed he had no idea how the collision occurred, but Verstappen was quick to point the finger in his direction.
When asked who was to blame the 19-year-old Dutch driver said: "Mainly Sebastian. He started squeezing me, maybe he didn't see Kimi on the left.
"That's not an excuse – if you're fighting for the world championship, you shouldn't take those risks to squeeze someone that much.
"What does he expect? When you're fighting for a world championship, you shouldn't do that. It was not very clever.
"I don't think it was a racing incident. At the end of the day, they take, in total, three cars out."