Ikeme and Elokobi both reported the abuse - which came from individuals among the crowd - to members of Wolves' management team.
A statement on the Wolves website reported that "the abuse which, respectively, came from behind the goal in the second half of Saturday's game at the Banks' Stadium and during the first half when Elokobi, a substitute, was warming up.
"The complaint relates to a small number of individuals in the crowd at Saturday's game and will not sour the good relationship that exists between the two clubs.
"Both Wolves and Walsall are fiercely committed to stamping out all types of discrimination within football and will vigorously investigate all allegations of racist abuse."
Speaking on Sky Sports News, Wolves boss Kenny Jackett added: "It's something that we don't want in football - it not part of either football or society and we'll do everything we can to eradicate and prosecute the indviduals concerned."
Walsall have pledged to co-operate with West Midlands Police and Wolves and have warned that anyone found guilty of racial abuse will be banned for life.
A statement on their website read: "Both Wolves and Walsall are fiercely committed to stamping out all types of discrimination within football and will vigorously investigate any and all allegations of racist abuse.
"Should anyone be found guilty of the above allegations, they will be issued with a lifetime ban from Banks' Stadium.
"As the matter is being investigated, the club can make no further comment at this stage."