The striker scored in the 60th minute at Old Trafford, turning home at the back post from Josko Gvardiol's cross after the goal was initially disallowed on the field for offside.
Following intervention from the video assistant referee, the goal was awarded, with Haaland ruled to have been played onside by Patrick Dorgu's boot.
There was debate, however, over whether Enzo Fernandez, who was in an offside position and dived at the ball in a more central position than Haaland, was interfering with play.
In a statement, Pro Ref said: "It was established that Enzo Fernandez did not play the ball and therefore that makes any offside offence subjective.
"However, on this occasion, the VAR did not recognise the likely impact of his position and should have recommended an on-field review.
"Contact has been made with Manchester United this evening to acknowledge what we deem is an error of judgement. A review of the incident will take place."
Manchester United defender Lisandro Martinez described the decision as an "injustice", while manager Michael Carrick said he was "confused" by the outcome.
The goal came after Manchester City had been reduced to ten men in the first half when Phil Foden was shown a straight red card by referee Michael Oliver for kicking out at United captain Bruno Fernandes, who was on the ground at the time.
When Haaland's goal was initially ruled out for offside, few questioned the call, with the City striker appearing to have drifted beyond United's defensive line.
The lines drawn by VAR showed Haaland to be onside owing to the deflection off Dorgu's boot, but it was the positioning and involvement of Fernandez that left pundits astonished and unsure whether it was a legitimate goal.
Gvardiol's cross took a slight deflection off Dorgu before finding its way to Haaland at the back post, while Fernandez was attempting a diving header in the middle of the six-yard box but did not make contact with the ball.
Fernandez appeared to be in an offside position ahead of Dorgu's touch, but the VAR deemed the goal legitimate as he had not played the ball, even as United defender Martinez closed in on the danger.
The Premier League's official Match Centre account explained on social media: "VAR checked the referee's call of no goal for offside - and determined that Haaland was in an onside position and recommended that the goal was awarded.
"The VAR also deemed that while in an offside position, Fernandez didn't play the ball."