The German was wearing a rainbow coloured t-shirt with the message "Same Love" on the grid ahead of the start of the race.
Three other drivers -- Mercedes' Valtteri Bottas, Ferrari's Carlos Sainz and Vettel's Aston Martin teammate Lance Stroll -- were also reprimanded for failing to remove their "We Race As One" t-shirts in time for the national anthem.
Vettel and the other drivers said they had forgotten to take their t-shirts off because of the onset of rain. They were all found to be in breach of Article 12.2.1.i) of the FIA International Sporting Code and given non-driving reprimands.
"We Race As One" is a platform launched by Formula One last year that counts diversity, inclusivity and sustainability as its core principles.
Drivers are free to wear apparel with a message that is supportive of the initiative's principles. But they were instructed to remove any such t-shirts before the national anthem and wear their race suits in a pre-race note issued by race director Michael Masi.
Hungary is set to put an anti-LGBTQ+ law that limits schools’ teaching about homosexuality and transgender issues to a referendum.
Vettel, who on Thursday wore shoes carrying a rainbow stripe, has spoken out against the legislation along with seven-time world champion Lewis Hamilton who called on Hungarians to vote against it.