"Some students became angry after they saw his remarks on Facebook where he said opposition leader Ilias Ali had no chance for freedom because he was caught by Sheikh Hasina," Trishal police chief Firoz Talukdar told AFP.
Ali, a regional head of opposition Bangladesh Nationalist Party (BNP), has been missing since mid-April. The BNP has accused state security forces over the disappearance - a charge denied by the government and the forces.
"He wrote that Ali would have been freed had he been caught by a jungle tiger. But this jungle tiger is Sheikh Hasina," Talukdar said, adding that if found guilty under sedition charges Molla could face a maximum life sentence.
Talukdar said police had sought the home ministry's permission to charge the 21-year-old English literature student. "We've completed our investigation and found that his Facebook remarks are seditious," he said.
Home minister Sahara Khatun told Bengali daily Prothom Alo the student would be charged with sedition.