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 Autosport.
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.
Photo by: Erik Junius
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.
He had previously been made an Officer of the British Empire in 2013, when Red Bull enjoyed a run of four consecutive title doubles from 2010.
“It was an unexpected distinction a decade ago to be presented with an OBE and to receive this second award, a CBE, is one for which I am hugely grateful and deeply honoured,” he said.
“It is a great privilege to lead and work alongside such a phenomenal team as Oracle Red Bull Racing and also to work in an industry that contributes so much to the UK economy.
“I am enormously proud of what we have achieved with Red Bull in Formula 1 and in the wider high technology arena, and I am hugely honoured to be recognised for that effort.”