Referee Bobby Madden inspected the pitch at Firhill at three o'clock on Friday afternoon and decided it was unplayable.
Aberdeen, who lost 3-1 at Inverness on Monday, were hoping to put some pressure on league leaders Celtic by closing their lead to goal difference at the top.
Celtic now have an opportunity to open up a six-point gap if they beat Inverness CT on Saturday, having played the same number of games as the Dons.
Thistle will be disappointed the match is off as they already have two games in hand over most of the teams around them, and because the team have not lost at home since October.
A statement from Partick read: "Following a pitch inspection by Bobby Madden at 3:30pm tonight's Ladbrokes Premiership match against Aberdeen has been postponed due to a waterlogged pitch.
"Anybody with pre-purchased tickets should retain them and further details about the re-arranged fixture will be released as soon as we have them."