Mackay was named as Uwe Rosler's replacement at the DW Stadium on Wednesday, despite currently being investigated by the Football Association for sending offensive text messages during his time at Cardiff City.
The 42-year-old's appointment has brought criticism from anti-discrimination group Kick It Out, and one of Wigan's primary sponsors has now announced they will no longer have a relationship with the club.
"Unfortunately, their recent appointment of Malky Mackay has put us in a position that we find untenable," Premier Range told BBC Sport.
"Mr Mackay is currently under investigation by the FA for sending text messages that are at odds with the general ethos here at Premier Range - and, it would seem, Cardiff and QPR feel the same as us.
"The texts Mr Mackay has admitted to sending are wholly unacceptable - and the thoughts expressed within them are a shocking reminder of a past we thought football had left behind.
"A team that would employ a man who expresses views such these is not the kind of team Premier Range wish to deal with."
Meanwhile, the FA has confirmed it has given no indication as to the outcome of their investigation into Mackay and his former head of recruitment at Cardiff Iain Moody.
To add to the furore surrounding Mackay's appointment at Wigan, chairman Dave Whelan has been accused of anti-Semitism following comments made to the Guardian.
Whelan is said to have told the newspaper there was not "a lot wrong" with anything Mackay had said in the text messages that are currently under investigation by the FA.