The football club said it was "hugely disappointed" after a fan was ejected from Firhill stadium.
Police Scotland said a 42-year-old man was arrested in connection with the Offensive Behaviour at Football and Threatening Communications Act following the game against Hibernian.
He is expected to appear at Glasgow Sheriff Court today.
Partick Thistle FC said in a statement: "The incident was dealt with very efficiently by both our stewards and Police Scotland, with the man in question swiftly removed from the stadium.
"He is now subject of a Police Scotland investigation in which the club will cooperate fully.
"Partick Thistle does not accept racism, sectarianism, homophobia or bigotry of any kind and anybody found to be using such language will be ejected and banned from attending games in the stadium. There is no place for bigotry at Firhill."
Partick Thistle won the Scottish Premiership match 3-1.