At least four other states are considering similar proposals.
Under the proposed legislation schools would have to conduct the drills at least five times a year. Students will be confined inside locked classrooms to practise taking refuge from and isolating intruders or armed students before police arrive.
The legislation has been co-sponsored by Democrat Minnesota senator John Marty. His assistant, Michael Brakke, said it was "galvanised" by America's second-worst school shooting at Red Lake high on a native American reservation in Minnesota last March.
A student shot dead a teacher, five students and a security guard, before turning the gun on himself.
The proposed statute would cut the number of fire alarm tests schools would perform annually from nine to five, to make time for the lockdown drills.
"We've done a great job with fire drills, but there's a need to deal with emergency management in the case of different crises," said Mr Brakke. "
It's not just natural disasters, but problems like shootings and bomb threats that we're dealing with."
"Lockdowns need to be practised," said Kenneth Trump, president of National School Safety and Security Services. "Crisis plans are no good sitting on a shelf collecting dust. They need to be exercised to make sure what's on paper works."
Kentucky, Michigan, Ohio and South Dakota are looking at similar measures.