Iran has come under mounting international pressure to ensure its investigation into the tragedy is full and transparent.
The authorities' handling of the air disaster has also angered some Iranians.
Videos posted online Monday purported to show hundreds of protesters taking to the streets for a third consecutive night, apparently shouting slogans against the Islamic republic.
Protesters chanted "Death to dictator" on Sunday, Fars news agency reported, a rare move for a country where media usually refer to demonstrators as "rioters" and refrain from publishing such slogans.
The protests have been much smaller than nationwide demonstrations against fuel price hikes that turned deadly in November.
Tehran for days denied Western claims based on US intelligence that the Boeing 737 had been downed by a missile.
It came clean on Saturday when Revolutionary Guards aerospace commander Brigadier General Amirali Hajizadeh acknowledged a missile operator had mistaken the plane for a cruise missile and opened fire independently.
At a televised news conference, the judiciary announced the first arrests had been made over the calamitous blunder, without specifying how many.
"Extensive investigations have been carried out and some people have been arrested," said spokesman Gholamhossein Esmaili.
The announcement came shortly after President Hassan Rouhani said everyone responsible for the disaster must be punished.
"For our people it is very important in this incident that anyone who was at fault or negligent at any level" face justice, Rouhani said.
"Anyone who should be punished must be punished.
"The judiciary must form a special court with a high-ranking judge and dozens of experts... The whole world will be watching," Rouhani said.
"It cannot be that only the person who pressed the button is at fault. There are others, and I want this to be explained to the people explicitly."
The Kiev-bound plane was shot down at a time when Iran's armed forces were on heightened alert after launching a volley of missiles at Iraqi bases housing US troops.
Iran fired the missiles in retaliation for a US drone strike on January 3 that killed Qasem Soleimani, the head of the Guards' Quds Force foreign operations arm.
Addressing that issue on Tuesday, Rouhani said while "the root of all sorrows goes back to America... this cannot be a reason for us not to look into all the root causes" of the air disaster.
The president also demanded officials explain why it took so long for authorities to announce the real cause of the air disaster.
"They must explain the whole process. From Wednesday morning when the incident happened until the meeting on Friday night of the Supreme National Security Council. They must explain this whole process to the people," said Rouhani.
"But more important than anything else, in my opinion, is that our people must be assured that this incident will not be repeated."
Iran has invited experts from Canada, France, Ukraine and the United States to take part in the probe into the air disaster.
On Monday night, Canada's Transportation Safety Board said its investigators flying to Tehran would be granted access to the wreckage and black box flight recorders of the downed airliner.
"There have been early signs that Iran is allowing the TSB to play a more active role than is normally permitted," its chair Kathy Fox said.
On the diplomatic front, Britain on Monday summoned Iran's ambassador to lodge its "strong objections" after its Tehran envoy Rob Macaire was briefly arrested for allegedly attending a demonstration on Sunday night.
But Iran hit back, calling for "an immediate halt to all interference and provocation by the British embassy".
The judiciary spokesman on Tuesday described Macaire on Tuesday as "an undesirable element" and said his "obligations under international treaties are clear".