The Fossano factory in Italy and the Oranienburg factory in Germany would be shut by the end of 2016, and Ballymena in Northern Ireland by mid-2018, the company said.
Michelin said increased competition and the economic crisis had "lastingly affected the European tyre market", especially for trucks and reconditioned tyres.
The closures will affect nearly 1,500 staff in total, the company said in a statement.
Michelin said it would make a one-off provision of €280 million ($307 million) in the current financial year to cover the cost of the closures.
The company said other European factories would take over some of the production currently handled by the three affected sites.
Michelin is among the world's three biggest tyre makers, along with Bridgestone and Goodyear.
It employs 65,000 staff in Europe, where 40 production sites account for 40 percent of worldwide sales.