The club said a safety inspection had taken place at Tannadice on Thursday that led to the decision.
Photos showed heavy snow on the pitch and touchlines, as well as in the streets surrounding the stadium.
A statement from the club read: “After prolonged snowfall and following a safety inspection in and around Tannadice this morning, tomorrow’s fixture at home to St Mirren has been postponed.
“A new date for this game will be announced in due course.”
St Mirren currently top the Championship table, with United in fourth, albeit with three games in hand.
The postponement means United’s next home game is likely to be on March 17 - a full 49 days after their last home fixture on January 27.