Mackay is currently under investigation from the FA over a series of offensive text messages apparently sent during his time as Cardiff manager.
The kitchen firm, who were the club's back-of-the-shirt sponsor, said it was put in an "untenable" position by his appointment.
Dave Whelan himself faced accusations of racism and anti-semitism today over remarks published in the Guardian. Whelan is quotes as saying that "Jewish people chase money more than everybody else" and that there was "nothing bad" about using the word "chink".
Simon Johnson, the former FA executive now currently chief exec at the Jewish Leadership Council, tweeted: "I call on Dave Whelan to withdraw and apologise for his use of disgraceful antisemitic language."
Anti-racism group Kick it Out yesterday questioned Wigan's appointment of Mackay in a strongly worded statement yesterday in which they claimed the Championship club had disregarded the FA's ongoing investigation.
Premier Range's statement in full:
Football is very close to our hearts here at www.premierrange.co.uk and we have always involved ourselves with local teams in one way or another.
We had a great run with Burnley FC and were delighted when they were promoted this season.
We thought that it was natural for us to move onto another local team with Wigan and we decided to sponsor their shirts.
Unfortunately, their recent appointment of Malky Mackay has put us in a position that we find untenable.
Mr Mackay is currently under investigation by the FA for sending text messages that are at odds with the general ethos at Premier Range.
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 as these is not the kind of team Premier Range wish to deal with.