The triple world champion, best remembered for his comeback from a fiery crash in 1976 that left him badly burned and scarred him for life, died last week at the age of 70.
Members of Lauda's family accompanied pallbearers carrying his remains into the gothic cathedral early in the morning. His wife Birgit and two of his sons placed Lauda's red-and-white driver's helmet on his coffin.
Fans then filed past the raised casket, which was flanked by candles and floral wreaths in the centre of the cathedral, many queuing outside for an hour or more.
"He was Niki, he is our national hero, our icon," mourner Marion Hahn said. "I have never done anything like this, to stand in line for someone for this long but I hope he rests in peace. He deserves it."
After several hours, the cathedral's doors closed and onlookers gathered outside, standing several deep behind police barriers.
Roughly 500 guests attended a Requiem Mass, which was also open to members of the public but took place behind closed doors.
Lauda's former McLaren teammate Alain Prost was due to give a reading from the Old Testament at the private ceremony, the Vienna archdiocese said.
Five-time world champion Lewis Hamilton - who raced to victory in the Monaco Grand Prix on Sunday in a helmet bearing Lauda's colours and name - was also due to join the congregation.
Fellow Austrian racing driver Gerhard Berger, Austrian-born star Arnold Schwarzenegger and two Austrian dignitaries -President Alexander Van der Bellen and recently ousted Chancellor Sebastian Kurz - will give short speeches at the end of the service.
A video sting scandal that felled the leader of the far-right Freedom Party and blew up Kurz's coalition government drew some attention away from the national hero's death.
"Rather than grief I feel it's good that we had a person like him in Austria, someone who influenced motor racing so much and who could have been a role model for politicians," mourner Ernst Kollensteiner said.
Lauda will be buried at a smaller private ceremony later in the day.
(Reporting by Francois Murphy; Additional reporting by Kirsti Knolle and Reuters TV; Editing by Andrew Heavens and Stephen Powell)
