The fans repeatedly chanted "basketball" at Smith-Pelly while he was in the penalty box Saturday night during a game against the Blackhawks. They were later ejected.
Capitals head coach Barry Trotz showed support for Smith-Pelly afterwards, and said the chanting was "disgusting."
The Capitals, Blackhawks, and NHL commissioner Gary Bettman all condemned the incident in separate statements.
Simmonds, who like Smith-Pelly is black, has also endured racism during his career. While playing in the Czech Republic during the 2012-13 lockout, an opposing team was fined after its fans directed racist insults towards him, and a fan in London, Ont., was fined for throwing a banana at him during an exhibition game on Sept. 22, 2011.