"The [Sunday] incident with Samba was simply outrageous and I've instructed our ethics committee to look into this," RFU chief Sergei Fursenko told reporters.
Media reports said that a banana was thrown at Samba from Lokomotiv's VIP box at the end of the match, won by the home team 1-0.
The 27-year-old Congo international, who joined the wealthy club from the volatile North Caucasus region from Blackburn Rovers last month, then picked up the banana and threw it back.
"I'm very sad that [the incident] was seen by kids," Samba told Anzhi's official website.
"It would be a bad example for them. I try not to think about racism too much. I just hope such a problem doesn't exist in global terms. Maybe I'm mistaken. This was the act of one stupid person. I don't want to react to it."
Sunday's drama was the latest in a series of racist incidents in Russian football.
Another Anzhi player, Brazilian full-back Roberto Carlos, was the victim of banana attacks at stadiums in St Petersburg and Samara last year.
Lokomotiv president Olga Smorodskaya denied any wrongdoing by her club's fans.
"I was at the stadium on Sunday and didn't see anything bad there. I was watching our fans and they conducted themselves in exemplary fashion during and after the match," she said.
"I would like to bring to people's attention that all these banana stories happen only with one club. No one saw anything. It all looks like a provocation.
"We have a lot of dark-skinned players on our team and have never had anything of this kind."
In 2010, Lokomotiv fans unveiled a huge banner with a banana cartoon, saying "Thanks, West Brom".
It was addressed to Lokomotiv's Nigerian striker Peter Odemwingie, who was playing his last game for the Moscow club before leaving for England's West Bromwich Albion.
