Machico is a municipality, parish and city in the southeast part of the island of Madeira, in the Autonomous Region of Madeira. The easternmost …Machico is a municipality, parish and city in the southeast part of the island of Madeira, in the Autonomous Region of Madeira. The easternmost municipality on the island, it is also the third-most populous area with a population of 21,828 in 2011. The town, proper, had a population of 10,894 in 2001.