The Firhill club announced on their Twitter feed that the match, which had been due to kick off at 5.30pm, had been postponed due to a waterlogged pitch.
Aberdeen take on St Johnstone at 3pm today and can knock Celtic, who will have a game in hand, off the top of the table.
The club made the announcement following a late pitch inspection following heavy rain overnight.
A tweet from the club’s official account read : “Unfortunately, despite best efforts of the ground staff, today’s game against Celtic has been postponed due to a waterlogged pitch.”
Partick say tickets purchased will be valid for the rescheduled match.