The drivers began their protest at 1:00 pm (1100 GMT), just seven hours before the official opening party for the festival which is expected to draw hundreds of thousands of people.
The drivers -- who are currently considered "unskilled personnel" -- are seeking recognition of their professional status.
The strike is expected to last until Sunday, meaning metro services would be reduced on Saturday when the Spanish capital holds a huge WorldPride parade which organisers say could attract up to one million people.
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The regional government of Madrid, which operates the metro service, has ordered drivers to provide a minimum service during the strike, which should ensure that "64 percent to 75 percent" of trains will be running".
The Gremial taxi federation had also urged its members to strike on Thursday and Friday against growing competition from ride-hailing companies like Uber and Cabify, but they called off their protest on Wednesday.
Thousands of taxi drivers had already protested across Spain in May, and they are particularly angry that San Francisco-based Uber is one of the WorldPride sponsors this year.
Madrid city hall predicts over two million people will take part in the festivities, which include free outdoor concerts, a high heel race and a beauty contest to elect Mr. Gay Pride Spain.