Unified Police Union (SUP) spokesman José María Benito told El Botelin that the medal had always been awarded posthumously to Civil Guard and police officers who have died in terrorist attacks.
"Give the Virgin Mary whatever you like, take some flowers, make her the patron saint of our people, but ,don't give her a police medal, least of all one reserved for officers who die in terrorist attacks," he said.
The furore began on Monday when Interior Minister Jorge Fernández Díaz issued General Order Number 2015.
In that order, he informed police of the "honorific" award at the request of the "Royal, Most Excellent, Most Illustrious brotherhood of the Worship and Procession of Our Lord Jesus and the Blessed Mary" with which the force works "in close collaboration, especially in events during Easter."
It was spotted and shared on Twitter by Fer Gonzalez, better known as Gonzo, a journalist for Spain's La Sexta TV channel.
De los creadores de Santa Teresa intercede por España, llega la Virgen q merece una medalla de oro al mérito policial pic.twitter.com/u4BnymkagN— fer gonzález gonzo (@a_lo_gonzo) February 24, 2014
Gonzalez wrote, "From the creators of Saint Teresa intercedes on behalf of Spain, comes the Virgin who deserves a gold medal of police merit."
The comment referred to an earlier controversy involving the interior minister.
In January Fernández Diaz said that "I'm sure that Saint Teresa is an important advocate for Spain during these tough times we're going through."
He added: "I'm sure that her efforts from above, where she is in great command, will assure success."
The latest medal is not the first to be given to an image of the Virgin Mary by the current government.
In 2012 it awarded Zaragoza's Virgin of Pilar the Great Cross of the Order of Merit of the Civil Guard.
Spain is a secular country but concern over religious interference in official Spanish affairs was expressed as recently as Monday by the Judges for Democracy Association.
It was moved to remind the government of the "secular" nature of the Spanish state after it was revealed that Carlos Lesmes, head of Spain's Supreme Court, had headed a Spanish delegation to the Vatican to see the Pope choose new cardinals.
A 2005 Eurobarometer poll found only 59 percent of Spaniards believed in God and 21 percent in a higher power, or close to Europe averages.