The club have confirmed both incidents took place at the Bescot Stadium during their 3-0 victory in League One on Saturday.
Elokobi raised the issue to Wolves' management team while warming up as a substitute in the first-half, while Ikeme alleges he was also abused in the second half of the match.
In a statement the club said: "Wolves have made an official complaint to Walsall and the Football Association after Carl Ikeme and George Elokobi were racially abused by individuals in the crowd at the game on Saturday.
"Ikeme and Elokobi both reported, to Wolves’ management staff, the abuse which, respectively, came from behind the goal in the second half of Saturday’s game at the Banks’s 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."
Meanwhile, Walsall also vowed to work closely with Wolves and the police to look into the alleged incidents.
"We are taking this matter very seriously and will fully co-operate with West Midlands Police and Wolverhampton Wanderers throughout this investigation," a statement on the club's official 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’s Stadium. As the matter is being investigated, the club can make no further comment at this stage."
