Abdullah Morsi, 19, and his friend were arrested on March 1 after allegedly being found in possession of two hashish joints while they were in a car parked by the roadside in Qalyubia province, north of Cairo.
The two were freed the next day pending investigation after agreeing to give urine samples, which the prosecution says tested positive.
A court in Banha, in Qalyubia province, on Wednesday handed down sentences of one year in jail and fines of 10,000 Egyptian pounds (around $1,400 or 1,025 euros) each.
The defendants can appeal the verdict.
Defense lawyer Mohamed Abu Leila said the case “was fabricated.”
“Rulings nowadays don’t deserve comment; the entire system is defective,” Abu Leila said.
Since Morsi was ousted by the army a year ago, the authorities have been accused of using the judiciary as a tool of repression.
Morsi himself and several leaders from his Muslim Brotherhood have been put on trial on charges that could lead to the death penalty.
Egypt, which on Thursday marks the first anniversary of the toppling of Morsi, has been roiled by unrest since his ouster.
A police crackdown targeting his supporters has sparked street clashes in which more than 1,400 people have died.
At least 16,000 others have been jailed with around 200 sentenced to death in speedy mass trials that have sparked an international outcry.