Officials say journalists who filmed Bowatte Indarathana's self-immolation could have tried to have him rescued.
The Media Ministry Secretary, Charitha Herath, said the monk had told at least one TV journalist of his plan.
Meanwhile, hardline Buddhist nationalists are hailing the dead monk as a hero for his act.
Mr Herath said any reporter who knew in advance of the monk's plans should have contacted the police.
"My issue is that if you have already [been] informed by somebody that he is going to commit suicide, you are supposed to at least inform others to get rid of that disaster," he said.
Venerable Indarathana was protesting against the slaughter of cattle and the alleged conversion of Buddhists by Sri Lanka's minority faiths.
He set himself on fire outside the holiest Buddhist shrine in the country - the Temple of the Tooth in the central city of Kandy. He died in intensive care in the capital Colombo the following day.
The monk - believed to be aged 30 - belonged to a Buddhist revivalist group which has been campaigning against the Muslim halal method of slaughtering animals.
The government condemned media outlets showing video of the incident.
The BBC's correspondent in Sri Lanka, Charles Haviland, says some viewers have criticised the extensive coverage the suicide received from a hardline Buddhist TV channel, Swarnavahini.
However, Sinhalese ultra-nationalist ministers in the government have praised the incident as an act of self-sacrifice for the good of the country, he adds.
Dozens of monks from the same group, Voice of Sinhala, and their supporters, staged a demonstration in Colombo on Sunday after the authorities rejected their demand for the monk to be given a state funeral.
Self-immolation by Buddhist monks in Sri Lanka is exceptionally rare, although many Tibetan monks have recently committed suicide in this way for political reasons.

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Dujardin, 30, set world records in winning the freestyle dressage and grand prix events last year.
The double Olympic and world champion will ride Uthopia instead of her usual horse Valegro in Wednesday's freestyle.
Brash, the first rider to complete the sport's grand slam, competes in the World Cup showjumping on 20 December.
Four members of the Whitaker family, John, Michael, Robert and William, are also set to compete during the week, while Ben Maher, another London 2012 gold medallist, seeks to defend his Grand Prix title on Monday, 21 December.
Wednesday 16 December
Live coverage of the World Cup dressage freestyle
Red Button, online & connected TV from 20:00 to 22:35 GMT
Thursday 17 December
Live coverage of the Olympia Puissance high-jump competition
Red Button, online & connected TV from 21:00 to 22:15 GMT
Sunday 20 December
Live coverage of the latest World Cup leg, plus highlights of the puissance high-jump competition
BBC Two, online & connected TV from 13:45 to 16:30 GMT
Monday 21 December
Live coverage including the Olympia Grand Prix
Red Button, online & connected TV from 18:45 to 22:25 GMT
Wednesday 23 December
Highlights of the week, including the Olympia Grand Prix
BBC Two HD, online & connected TV from 11:00 to 12:00 GMT
All programmes times subject to change

Bevan, 18, who won team silver at the World Championships in Glasgow last month, has had surgery.
He broke his left tibia and fibia after landing on a concrete floor in what he described as a "freak accident".
He wrote on Instagram that the injury was heartbreaking and the "lowest low" after "such a high of the Worlds".
British Gymnastics' medical team is expected to issue more information on the teenager's injury on Tuesday.
It is yet unclear whether the Essex-based gymnast has a chance of returning to fitness to secure one of three individual spots available on the British team, as well as a place in the team event, at next summer's Olympics in Rio de Janeiro.
"All my emotions just erupted and I've found myself constantly in tears," Bevan said.
"This may be a big stepping stone to overcome but most, if not all, successful athletes have had to overcome adversity to reach their goals.
"That moment at the World Championships I will never forget and it's something I want to feel again."
Sri Lanka is to investigate the role of the media in the death of a Buddhist monk on Saturday, the day after he set fire to himself.
[NEXT_CONCEPT]
Olympic champions and world number ones Charlotte Dujardin and Scott Brash head the field at the London International Horse Show at Olympia on Tuesday.
[NEXT_CONCEPT]
British gymnast Brinn Bevan suffered a double leg break while vaulting on Saturday, putting in doubt his hopes of competing at next year's Olympics.