Ross County said it was appalled by the actions of some fans during a minute’s silence at Dingwall on Saturday.
Jeers and several smoke bombs were fired in the prison stands before County’s fourth-round Scottish Cup home game against Livingstone.
The moment of silence was held in memory of former Scotland international, Manchester United and Manchester City striker Dennis Law, and Gordon Seaton, who played for County in the 1970s and 1980s.
Ross County said the county and police are investigating the incident, which could result in charges or bans from the stadium.
Several young people were reportedly told to leave the field.
“This organization showed complete disrespect during a moment of silence for a former player and another national football player,” the club said.
“Their conduct was reprehensible and, in addition to the jeers and inappropriate noise, several smoke bombs were ignited, which was completely dangerous and reckless and could have caused injury to those in the stands.
“For the avoidance of doubt, Ross County FC does not condone any place at our club where such unacceptable behavior takes place. We encourage anyone with information to contact us with detailed CCTV footage or other video recordings. Please contact the club as we are investigating to identify the culprits,” they added.
Championship side Livingston won 3-2 after extra time.
Law, who died on Friday aged 84, was born in Aberdeen and was the only Scottish player to win the Ballon d’Or, which is awarded annually to the world’s best footballer.