The club said any fans found guilty of racism would face the strongest possible action, and its chairman wrote an open letter on Tuesday singling such fans out and saying Chelsea would continue to fight discrimination.
UEFA said it had initiated action against Chelsea according to article 31 (4) of their disciplinary regulations.
"UEFA has today announced it has commissioned an ethics and disciplinary inspector to conduct an investigation in relation to the alleged racist incidents that occurred at last week's Europa League group stage match between Vidi and Chelsea," UEFA said in a statement.
It said it will issue the results of its investigation by mid-January.
Racism has long been a source of controversy in sport, and efforts to stamp it out both among supporters and within sports organisations have been increasing at all levels.
Some Chelsea supporters have been involved a number of such incidents recently.
Earlier this month, four fans were banned from the club's matches pending a police investigation after alleged racist abuse of Manchester City forward Raheem Sterling.
Three men were then spoken to by transport police after reports of anti-Semitic chanting on a train after a match between Brighton and Hove Albion and Chelsea last weekend at the Amex Stadium.
In an open letter, Chelsea chairman Bruce Buck said racist fans were behind the times and were an embarrassment to the club.
"A deeply unpleasant but vocal minority which refuses to join us in the 21st century has shamed the great majority of our decent, well-behaved fans," Buck wrote.
"I have spoken to Chelsea fans and supporter groups, all of whom are in full agreement that the behaviour we have witnessed is unacceptable, hurtful and does not represent the club or the majority of those who follow our teams home and away.
"We are committed and determined to be a force for good and not a symbol of society's wider problems... clearly, there remains a way to go on this journey, but we will not rest until we have eliminated all forms of discrimination from our club."
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Hugh Lawson)
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