The 4.4-metre-long (14-ft) cloth is on show until 24 June.
Viewings are free but must be booked. One million people have already signed up.
Some devotees believe the shroud is the burial cloth of Jesus Christ. Sceptics point to carbon dating that suggests it is a medieval forgery from the 1300s.
Scientists have not agreed on how the image of a man was imprinted on the cloth.
Turin Shroud: See it in detail
Pope Francis will be among those to view the shroud, during a visit to the northern Italian city on 21 June.
The last public viewings were in 2010, when 2.5 million people came to see it.
The Church has not officially claimed that Christ's body was wrapped in the shroud, preferring instead to focus on what it means to those who see it.
"Whether you believe or don't believe, there is no doubt it is something special," an Italian man who was among the first visitors on Sunday told the AFP news agency.
Earlier this week, Archbishop of Turin Cesare Nosiglia said: "What counts the most is that this shroud... reflects in a clear and precise manner how the gospels describe the passion and death of Jesus.
"It is not a profession of faith because it is not an object of faith, nor of devotion, but it can help faith."
Archbishop Nosiglia said that many of those coming to see the shroud would be returnees.
"That means there is a fundamental need in people's hearts to renew this incredible experience that they had the first time they saw it," he said.
"Even non-believers will come. It's an occasion that brings everybody together."
The shroud is displayed in a climate-controlled case for 12 hours a day in Turin's Cathedral of St John the Baptist.

They were evicted from the British overseas territory in the 1960s to allow the UK government to lease Diego Garcia to the US to use as an airbase.
Many residents of what is the largest of the Chagos Islands ultimately resettled in Crawley, West Sussex.
The petition demands the islanders' right to return home is respected.
TV presenter Ben Fogle, patron of the UK Chagos Support Organisation, handed in the petition, which had been signed by more than 2,500 people.
"Diego Garcia, which is one of the main prohibiters to the islanders returning, is up for renewal in the next year or so," Mr Fogle said.
"We're asking this government to think about whether these islands should belong to the people who inhabited them for a very long time, or to the US government who have used it for renditions - for effectively torture."
He said he had visited the islands and found "houses still as they were left" and "the graveyard strangled by vegetation having been left untended".
"For me, being a Brit, it was probably one of the things I'm most ashamed about, that I'm part of a country that forcibly evicted these people and is now refusing their right to return," he said.
Mr Fogle added: "How wrong is that, that I've been able to be there and they can't?"
Henry Smith, the Conservative MP for Crawley, said: "I think we can't turn back time but what we can do is rectify the problem as soon as possible."
A Foreign Office spokesman said: "The government is committed to its ongoing review of resettlement policy towards the British Indian Ocean Territory."
The Turin Shroud has gone back on public display in the Italian city's cathedral, after a break of five years.
[NEXT_CONCEPT]
A petition calling for residents of the Chagos Islands to be allowed to return to their Indian Ocean homeland has been handed in to Downing Street.