A salesman at the shop on Glasgow's Argyle Street was secretly filmed selling cigarettes to a 14-year-old boy who was a volunteer for Glasgow City Council.
The teenager was not asked for proof of age.
Tesco pled guilty at Glasgow Sheriff Court to selling the product to a 14-year-old boy on March 5, 2013, at its Express store.
Sheriff John McCormick fined the supermarket £300, reduced from £450 because of the guilty plea.
The court was told it was the duty of Glasgow City Council to check retailers follow the rules of the law and do not sell products to underage customers.
Procurator-fiscal depute Derek Buchanan said the council's trading standards unit arranged for a volunteer to go into the shop. He said the boy was accompanied by someone from the council who was secretly filming.
Ray Gribben, defending, told the court: "I believe it is the first prosecution of its kind in Scotland. Tesco wish to offer a formal apology to the court for this offence."
The sheriff told Mr Gribben he took into consideration Tesco's quality of staff training and its good history.
A spokesman for Tesco said: "Tesco takes tobacco legislation very seriously and has rigorous procedures in place to prevent the sale of tobacco to minors.
"We provide support for colleagues in our stores to make sure they understand their role and their personal responsibility. This ensures that cases like this one occur very infrequently."