The Spurs captain picked up a knock during their Europa League victory over Qarabag in midweek but Ange Postecoglou was hopeful he would return in time for Sunday's clash.
However, the short turnaround proved too much for Son and he was left out of the matchday squad with Timo Werner taking his place for his first Premier League start of the season.
Despite not being able to call on their talisman Spurs ran riot against Erik ten Hag's hapless side at Old Trafford, with Brennan Johnson firing them into the lead after just three minutes.
Goals from Dejan Kulusevski and Dominic Solanke secured what was a comfortable victory for the visitors but the scoreline ultimately belied just how many chances they created.
Jamie Redknapp claimed Tottenham's win at Old Trafford could have been even more emphatic if Son Heung-min had been fit to start
Speaking following the game Redknapp insisted the result could have been even more emphatic if Son was fit to start.
'They're brave,' the 51-year-old said of his former club.
'[Postecoglou] could have played Bissouma as a defensive midfield player. He does take risks.
'If Son would have played today it would have been six. It was a statement win. There have been some really good performances.
'Kulusevski is full of confidence. He's got that pace. He's looking like a complete midfield player.'
Werner's blistering pace allowed him to be a consistent thorn in United's side but his finishing repeatedly proved to be lacking in the most decisive moments.
With the score still at 1-0 during the first half, the former Chelsea forward found himself one-on-one with United goalkeeper Andre Onana.
The onrushing 'keeper did well to block the effort but Werner will have been disappointed not to have doubled his side's lead.
Another massive chance came Werner's way following the interval, but once again his effort was denied by Onana, with the goalkeeper then scrambling brilliantly to deny Solanke from close range.