The lasagna was confiscated before the other boy had a chance to eat it Monday in the cafeteria at Gratigny Elementary School.
Police said it was unclear whether the boy even knew what he was carrying, although he tried to hide the bag when the monitor approached.
The boy "may have said it was oregano," said Mayco Villafana, spokesman for Miami-Dade County Public Schools.
Police and child welfare authorities were investigating the boy's family. "The focus is on the child's environment and what issues could have led to a child having a bag of marijuana in school," Villafana said. Police also were looking into whether an older friend may have asked the boy to hold the bag.
Also on Monday, authorities in Indianapolis said a 4-year-old boy took crack cocaine that police said was worth up to $10,000 to his preschool class and showed it to classmates, saying it was flour.
Teachers realized it was cocaine and called authorities.
"This could have killed these kids," said police Sgt. Roger Tuchek.
Indianapolis police said Tuesday they were still seeking the boy's parents, Kenneth Lee Green, 24, and Andrea D. Jackson, 23. Jackson was wanted on a warrant for failing to appear in court, court records showed. Green had been convicted of carrying an unlicensed firearm, resisting law enforcement and marijuana possession.