The Bluebirds are currently 15th in the Premier League, four points clear of the relegation zone, after running away with the Championship title last season.
But, despite looking set for a relegation battle, Tan is wary of committing any more money to the transfer pot after going £15 million over budget in the summer and criticised Mackay for speaking publicly of his targets before knowing if he would be backed.
"Tan Sri Vincent Tan was extremely upset to read quotes from the manager concerning the possibility of new recruits, before he had been informed whether funds would be made available," chief executive Simon Lim said in a statement.
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"His view is that, due to the funds already committed - including the originally authorised summer transfer budget of £35m that rose to £50m in total, including add-ons - the manager has been fully supported.
"The overspending of £15m has upset Tan Sri greatly, resulting in the removal of Iain Moody as head of recruitment. As such, he has stated that not a single penny will be made available in January.
"Having been the highest-spending promoted club and the seventh-highest spender in the Premier League last summer, the owner believes that the manager has been given the best possible chance of retaining our Premier League status."
The former Watford boss said after Saturday’s 1-0 win against West Brom that he would like to bring in new recruits across all areas of the pitch.
"I would look to strengthen all three departments in terms of a defender, a midfielder and an attacking player," Mackay told reporters. "I will talk to my chairman [about January] who will then discuss it with his board of directors and our owner and I will take my lead from them.
"It's up to them then what financially they want to spend in January. I've got my lists of players, whether they be permanent targets or loans for various positions. We've got to try and strengthen again."