The Briton presided over the most dominant season in Formula One history last year, with Max Verstappen taking his third title in a row and the team winning 21 of 22 races.
"After being made aware of certain recent allegations, the company launched an independent investigation," Red Bull said.
"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."
The Times newspaper reported Horner had been accused of inappropriate behaviour by a female colleague, who complained to the team's parent company.
There was no comment from the team but Horner, who is married to former Spice Girls singer Geri Halliwell, told Dutch newspaper De Telegraaf that he completely denied the allegations.
