He later tweeted, apparently joking: "I was really drunk for the interview". He also tweeted he was "Drunk AF".
Others wondered if he had suffered a minor stroke.
Fellow commentator Scotty Stevenson added : "I don't think he has had a stroke. Think he was frozen by the windchill."
SKY spokesperson Kirsty Way rejected the suggestion Mulligan was drunk.
"We had a work around cable mic for Andrew at halftime," Way told NZME.
"He was dealing with a lot of echo and as a result his speech was unclear. He was not drunk."
Way said Mulligan tweeted a "joke" about being drunk "in response to other texts".
"We have no further comment."
Mulligan is best known as a main host of the Crowd Goes Wild, the offbeat Sky sports magazine programme.