The Blues ran out 5-0 winners on the night to progress to the quarter-finals of this year's competition, but the contest has been marred by these serious allegations.
The Premier League giants claim that a player, whom Goal understands to be Hudson-Odoi, was targeted by a small section of Kiev fans towards the end of the game.
Chelsea released an official statement on their website on Monday afternoon which reads: "We can confirm a report of racist abuse directed at one of our players in the final minutes of the match in Kiev from a small section of home supporters. We wholeheartedly condemn such abhorrent behaviour.
"The matter was reported to the referee at the final whistle and the chairman and club secretary spoke to the UEFA match delegate immediately after the match. We expect UEFA to conduct a fulsome investigation and we will provide full cooperation."
This incident comes four years after Kiev were hit with a two-match stadium ban for racist attacks on fans during a Champions League tie against Chelsea.
Dynamo were charged with racist behaviour, blocking the stairways and crowd disturbance, while video footage emerged of an attack on four black men at the fixture between the two clubs in Ukraine.
This time around the Kiev fans have allegedly aimed their abuse specifically at Hudson-Odoi, with monkey-chants heard in the home stands as the match neared its conclusion.
The 18-year-old informed Chelsea captain Cesar Azpilicueta about the incident and he then reported it to referee Tobias Stieler.
It is highly likely that Kiev will once again face serious sanctions due to the actions of their supporters, but UEFA have not yet commented on the incident.
Hudson-Odoi showed great strength of character to play a starring role in an intimidating atmosphere at the Olimpiyskiy National Sports Complex, scoring the final goal in a comfortable victory.
Chelsea have been drawn against Slavia Prague in the last eight of the Europa League, with the first leg set to take place on April 11.