Visiting supporters had to make a 268-mile trip each way for the Championship clash at Ewood Park.
All Pompey fans would have had to begin their journey before finding out the match was called off.
They were told to head home following an 11am pitch inspection by referee Farai Hallam.
Torrential overnight rain left the pitch waterlogged, with Rovers confirming the decision in a statement.
The club said: "Today's Sky Bet Championship encounter against Portsmouth has been postponed due to a waterlogged pitch.
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"Following torrential rain in the area overnight, match referee Farai Hallam conducted a pitch inspection and deemed the Ewood Park surface unplayable.
"A new date for the fixture will be announced in due course."
However, fans were left furious with the decision being made so close to kick-off despite Pompey fans facing a mammoth journey to Ewood Park.
Reacting to the postponement, one supporter wrote on X: "That's so poor on Pompey fans. That journey is horror just to be told a few hours before kick off that it's off… a championship club by the way."
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Another added: "In 2024, at Championship level, this should be a points deduction."
A third fan also commented: "Championship club having a game called off due to the weather is embarrassing, you should be relegated with immediate effect."
Meanwhile, one more fumed: "How embarrassing is that, rain getting a Championship fixture called off almost four hours prior to scheduled kick off, really poor if a pitch at that level can't be expected to cope with heavy rain."
The match was the only Championship fixture postponed from Saturday's 10 scheduled matches.
There were two other matches in the Football League to fall foul of the weather, though.
In League Two, Bradford vs Accrington was postponed due to heavy snowfall and rainfall at Valley Parade and in the surrounding area.
Fleetwood vs MK Dons, also in the fourth tier, was called off at 10.45am following a pitch inspection.