Visiting player Christian Mbulu, who was an unused substitute during the match, was targeted as the teams performed their pre-match warm-up routines on the pitch.
Video footage which shows as many as 20 fans in the stadium’s main stand shouting comments at the 22-year-old has been handed over to Police Scotland.
Hearts told BBC Scotland that they were aware of the incident and were “cooperating fully” with the police.
A statement from Hearts added that the club “abhors racism and all forms of abuse, and the individuals in question will receive indefinite bans from Tynecastle Park”.
A police spokesman said: “Police Scotland can confirm that two subjects were arrested at the Hearts v Motherwell match. A report will be sent to the Procurator Fiscal.”