Police said one person was killed in the breakout at the prison in Apatzingan, about 330km northwest of the capital Mexico City.
Some of those who escaped are believed to be linked to one of Mexico's most violent drug cartels.
"It was very well planned. From start to finish it lasted between five and seven minutes," said police investigator Hector Elias.
A statement from the Michoacan Attorney General's Office said one of the prisoners, Fernando Coria, was shot by a guard as he tried to flee and three others were recaptured.
"Around 15:20 approximately 10 Suburban-type vehicles with darkened windows and flashing lights, disguised as official vehicles, arrived at the jail," Elias said.
"Around 30 masked men got out, wearing uniforms from the state and federal police and the Mexican army, all heavily armed," he added.
The jailbreak may have been organised by the powerful Gulf drug cartel, based in the northern border state of Tamaulipas and headed by Osiel Cardenas, who was arrested last March.
Among the fugitives are five suspected gunmen arrested in November on murder and kidnapping charges.
Michoacan has seen a wave of violence in recent months in what locals say is a turf war between the Gulf cartel and a local gang known as the Millennium. Authorities have had mixed results in trying to deal with the situation.
Cardenas' seizure came one year after the arrest of Benjamin Felix Arellano, the head of the Tijuana cartel, and the killing of his brother Ramon.
But in January 2003 troops seized and shut the offices of a federal anti-drug police unit on the grounds that police officers were in the pay of drug gangs.
And authorities have failed to recapture Joaquin Guzman, the head of the Sinaloa cartel since his 2001 jailbreak.
Mexico is a major grower of marijuana and opium poppies and is also one of the main routes for Colombian cocaine headed for the United States.