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More than 100 students had gathered to perform afternoon prayers when the multistorey building suddenly collapsed, state news agency Antara reported, citing a witness.
East Java police told reporters that rescuers evacuated at least 79 victims from the incident at the Al Khoziny Islamic boarding school in the town of Sidoarjo.
At least one victim had died following the incident.
Authorities are working to establish how many victims are still at the scene.
Lax construction standards have raised widespread concerns about building safety in Indonesia.
Earlier this month, at least three people were killed and dozens injured after a building hosting a prayer recital collapsed in West Java.
Meanwhile, teenagers rehearsing for a musical show were among seven people killed in Cirebon, east of Jakarta, in 2018 when the building they were in collapsed.
At least 75 people were also injured the same year when a mezzanine floor at Indonesia's stock exchange building in Jakarta collapsed into the lobby.