The bilingual public school bearing the Baroness' name will open its doors in the next academic year with space for 75 pupils.
The decision to name the school after Margaret Thatcher was announced by a spokesperson for Madrid's ruling Popular Party (PP) government Salvador Victoria on Thursday.
The school in the capital's Barajas district will be one of two new institutions built as part of a wider restructuring progamme, Victoria said.
But the naming of the school has raised the ire of some, Spanish daily 20 Minutos reported on Friday.
"Last year they (the Community of Madrid) changed the laws so they would have the final say in the naming of colleges," José Luis Pazos, spokesperson for the local Federation of Parents Associations (FAPA) told The Local.
"Before that the individual school councils chose their names, with input from staff, and parents and students," said the spokesperson.
"Now the regional government has the final say, and there are no limits on the names they use. It's all ideologically based.
"My organization doesn't have a personal position on what names they use," explained Pazos.
"But we do object to individual schools not be able to choose what they are called."
Twitter commentators also expressed their surprise at the move to label the school after the former British Prime Minister.
"A public school with the name of Thatcher. NONSENSE," wrote Twitter user Alonso.
"Madrid baptizing a public school with the name Thatcher, the enemy of public schooling. Long live coherency," said Twitter user @DyBuenaletra.
Meanwhile, United Left (IU) politician Alberto Garzón tweeted: "These are the same people who refuse to take down Fascist symbols in Spain.
The ex-Prime Minister died on April 8th at the age of 87.
Lady Thatcher was the first female British Prime Minister.
She was also the first British Prime Minister to make an official visit to Spain, in 1988.
In April the city of Madrid proposed naming a street after the former UK PM, a move which drew strong criticism from opposition parties.
Baroness Thatcher, nicknamed 'the milk snatcher' after putting an end to the distribution of free milk to schoolchildren during her time as Secretary of State, was Prime Minister in Britain from 1979 until 1990 and became known as the "Iron Lady" for her uncompromising style.
She earned the adulation of the right and the enmity of the left for her actions during the British miner's strike, and for her political views espousing sweeping cuts and a smaller role for the state.