The education board of Suita City, Osaka Prefecture, says local elementary and junior high schools will be open on Monday as soon as they are ready.
The announcement follows the arrest of a man who allegedly attacked a police officer and stole his loaded pistol on Sunday.
After the incident, police called on local residents to refrain from going out unless absolutely necessary.
The board said elementary schools will not hold any classes on Monday afternoon as the normally provided school lunches are unable to be prepared.
Education authorities in Osaka initially planned to have students from 35 public high schools stay at home.
But following the arrest, schools will start classes at their discretion.
Eighteen public schools for children with special needs will be closed for the day.
Kansai University's Senriyama campus and Osaka Gakuin University have cancelled their Monday morning classes, but plan to hold classes in the afternoon.