The opposition Kaleme website reported that a bus carrying opposition supporters to Qom was stopped and some of those on board arrested. It also reported some small clashes following the funeral.
"The police cracked down on people who were shouting [anti-government] slogans in front his house and people threw stones at them," the website said.
'Orderly and peaceful'
But Sadegh Zibakalam, a politics professor at Tehran University who attended the funeral, told Al Jazeera it had passed off peacefully.
"There was a huge crowd of both government and supporters of Montazeri ... people had come as far as from Tabriz and other very distant cities," he said.
"There were anti-government slogans but the crowds were very orderly and behaved very peacefully. There were huge government security forces, but they also kept away from he crowd and the procession."
Mohammed Shakeel, an Iran Analyst with the Economist Intelligence Unit, said that there was a potential for unrest with the funeral coinciding with heightened tensions around a major Shia Muslim festival.
"This almost adds a momentum in its own right to the Ashura commemorations," he told Al Jazeera from Dubai.
"The opposition are going to, not necessarily use, but utilise the death of Ayatollah Montazeri to propogate the whole opposition element and the ideas they stand for.
Foreign media were banned from covering the funeral ceremony.
Ahead of the funeral, Mousavi and Mehdi Karroubi, who were both defeated in June's disputed presidential poll, called for a national day of mourning.
"We invite all saddened religious people mourning the death of this pride of the Shia world to take part in the funeral of this legend of endeavour, jurisprudence and spirituality," Mousavi and Karroubi said in a joint statement published on the Kalme website.
Mousavi later arrived in Qom to attend the burial in the shrine of Masoumeh, a revered Shia figure.
In the wake of the street protests that followed the election dispute, Montazeri was referred to as the spiritual leader of the opposition.
In August, Montazeri described the clerical establishment as a "dictatorship", saying that the authorities' handling of street unrest after the disputed re-election of Mahmoud Ahmadinejad, the president, "could lead to the fall of the regime".
He was also an architect of the 1979 Islamic revolution but fell out with the Iranian leadership in the 1980s.
Montazeri passed away on Sunday in Qom after suffering a cardiac arrest.
Videos posted on the internet prior to the funeral appeared to show hundreds of Montazeri's supporters taking to the streets of Najafabad, his birth town, to mourn his death.
Baqer Moin, an Iranian journalist and author, told Al Jazeera that Montazeri's absence would be "greatly felt across the country", among people on both sides of the political divide.
"He was the most heavyweight among them [the reformists]. He had great popularity because he was a humble man, he was a simple man ... and above all he was very courageous," Moin said.
"He didn't fear expressing his views, critical of the current supreme leader or the policies of the government."
Ghanbar Naderi, a journalist for the Iran Daily newspaper, told Al Jazeera: "This is huge blow to the reformist camp, because he is unreplaceable and nobody is happy to hear about his sad demise.
"He used to say that religion should be separated from politics, because in this way, we can keep the integrity of religion intact."
But Seyed Mohammad Marandi, a political analyst at the University of Tehran, told Al Jazeera in August that Montazeri said "the same thing for around 25 years".
"After his inner circle was discovered to be linked to Mujahidin terrorists based in Iraq, he was isolated by the reformists," he said.
"He is not a major player and has always been very critical," Marandi said.