The punishment followed Rodriguez's social media rant in which he complained that his children had not been able to watch him play at the Santiago Bernabeu Stadium on Saturday.
The Balaeric Islands club issued a statement saying Rodriguez "has been suspended from duty and pay," and that the club "has stripped him of his captaincy with immediate effect."
Rodriguez, who joined Mallorca in 2018 and has made over 250 league appearances for the club, posted an Instagram photo of his family at the stadium, venting his anger at not playing.
"An important lesson and piece of advice for them: Never expect anything from anyone, especially these days, when meritocracy, culture, and respect for hard work are lacking," Rodriguez wrote. "Don't do things expecting something in return. Do it for yourself and your passion."
The midfielder's anger appeared directed at coach Jagoba Arrasate's decision to give recently signed forward Jan Virgili playing time in the 87th minute instead of him.
In a follow-up open letter published by Spanish media, Rodriguez said: "What I can't accept is the lack of respect for commitment and dedication.
"It hurts when a player who just arrived, with just one training session, has the opportunity to play ahead of teammates who have spent years defending this jersey with sweat and dedication."
Rodriguez has not commented since the club punished him.