The energy drinks company said that an external barrister had been appointed to probe the complaints, as it emphasised it was taking the matter seriously.
Red Bull did not detail the nature of the allegations, but Horner himself has strongly denied any wrongdoing.
A statement issued by the Red Bull company on Monday said: "After being made aware of certain recent allegations, the company launched an independent investigation.
"This process, which is already under way, is being carried out by an external specialist barrister.
"The company takes these matters extremely seriously and the investigation will be completed as soon as practically possible. It would not be appropriate to comment further at this time."
Speaking to Dutch newspaper De Telegraaf, Horner said: "I completely deny these claims."
The Red Bull F1 team was unavailable for immediate comment when contacted by Motorsport.com.
Horner has been Red Bull's team principal since 2005 and is coming off the back of one of the most successful seasons in F1 history.
As well as helping Max Verstappen to his third consecutive F1 title, Red Bull won 21 out of 22 races as it dominated the championship.
Horner's achievements in F1 led to him being awarded a CBE in the recent New Year's Honours list, for services to motor racing.