According to the club, the teenager reported the incident to a member of Forest's staff at half-time after he claimed to have heard what he believed to be racist chants from a section of home supporters at the New Den.
Chalobah, who arrived at the City Ground from Chelsea in September, scored Forest's equaliser in Tuesday's Championship game, which ended 2-2, but was substituted late on.
A statement from Forest said: "At half-time, [Chalobah] told Forest's deputy manager Ned [David] Kelly that he believed he was subjected to racist chanting from a section of the home support in the first half.
"The 18-year-old, who claims to have been initially subject to verbal abuse from the same section after receiving treatment for an injury in the opening minutes, was upset by the alleged abuse and struggled to keep his concentration during the interval as a result
"Nottingham Forest treat any incident of this nature extremely seriously and will be liaising closely with the relevant authorities in their investigation of this issue.
"Both clubs are in communication regarding the alleged incident and hope to uncover the truth as quickly as possible for all concerned parties."
Millwall released a statement of their own, which suggested that Chalobah had declined to make an official complaint at the time.
However, the club have said they will provide assistance if the police chose to intervene.
"In the light of the player's subsequent decision to raise the issue once more, Millwall football club will assist and support any police investigation that may ensue, and if evidence of racism comes to light, do everything possible to ensure the perpetrators are brought to justice and receive due penalty," the statement read.
"However, we are disappointed that the chances of substantiating the allegations have been significantly reduced due to the fact they were not deemed serious enough for an official complaint, which would have led to immediate police involvement, to be made at the time."