The pair have been arrested for alleged racist chanting believed to have been directed towards Boro's Egyptian striker Mido during the 0-0 draw against Newcastle at The Riverside last Saturday, 29th November.
"Middlesbrough FC has a very strong anti-racism stance," a Boro spokesperson has said.
"The club adopts a zero-tolerance attitude towards racism and, working with the police, we will not hesitate to ban supporters identified as directing racial abuse against players or other fans, as we have in the past.
"Middlesbrough Police have confirmed that two individuals were arrested at the game for racial chanting and have been given a court date."