Massa, who was already fuming after a near-miss between the two in qualifying, confronted Hamilton after the race, in which the Briton's McLaren had clipped his Ferrari while attempting to pass.
Hamilton collected a drive-through penalty for causing the collision but still finished the race fifth while the Brazilian, who limped back to the pits with a punctured rear tyre, was ninth.
Massa blamed Hamilton for "destroying" his race and was unable to mask his anger when the pair came face-to-face as they conducted interviews afterwards.
He slapped his rival on the shoulder before spinning him round, offering a sarcastic 'thumbs-up' sign and telling him "good job, very good job".
In response, Hamilton shouted after a departing Massa, "Don't touch me man. Don't touch me."
Prompted by an interviewer to comment on Massa's actions, Hamilton simply replied, "Well, there you go", before promptly leaving without speaking to the press again.
Massa, though, was more forthright and just 24 hours after having accused the Briton of "not using his mind" in qualifying, he again vented his anger.
"I told you yesterday [Saturday] that he cannot use his mind...even in qualifying, so you can imagine in the race," the Brazilian said.
"In qualifying he tried to do a Superman on the out-lap, you know? And today [Sunday] he tries to do the same in the race."
Sweat dripping from his face in the Singapore heat, Massa continued: "He could have caused a big accident. He touched my wheel on a straight - 300 kph, and he punctured my tyres, so he destroyed my race."
"(He paid) for that because he had the drive-through, (but) that's the problem. He doesn't understand even paying for a problem.
"It is important the FIA is looking, and penalises him all the time he is going in the car, because he cannot be thinking about it."
Massa looked exasperated when asked if he would speak to Hamilton about the situation.
"I tried," he replied. "But he don't listen to me...he don't listen maybe to even his father, so you imagine myself."
Hamilton, who has repeatedly had to defend his aggressive style while also making regular trips to the stewards, and Massa have been at odds since the Monaco Grand Prix in May.
The two collided in that race, with Massa retiring. Hamilton was also handed a penalty in Monaco after colliding with Williams driver Pastor Maldonado.
Hamilton and Maldonado were involved in another incident in qualifying for the Belgian Grand Prix last month, while the 2008 World Champion also collided with team-mate Jenson Button at the Canadian GP in June.
Massa, who lost out to Hamilton by a single point in the 2008 championship, called on the FIA after the Monaco Grand Prix to teach the Briton a lesson "or he will not learn".
Ferrari team principal Stefano Domenicali was more philosophical about the clash.
"What can I say? I think maybe Lewis was a little bit too aggressive in that corner but that's part of the racing," he said. "He received the penalty and he was in front of us again.
"It ruined Felipe's race...that's part of the racing."
Not for the first time this season, McLaren team principal Martin Whitmarsh was forced to defend Hamilton.
"Felipe approached Lewis in the post-race TV interview enclosure and grabbed him slightly aggressively," said Whitmarsh.
"That riled Lewis, understandably so, but he acted with commendable restraint and walked away from any potential confrontation.
"Later, he decided to walk away from talking about the incident too because he didn't want to escalate the situation. He did absolutely nothing wrong."