Scottish Football hit by bad weather
Games hosted by Raith Rovers, Cowdenbeath, Berwick Rangers and Stirling Albion also failed Saturday morning pitch inspections.
The match at Caledonian Stadium, where Hearts were due to be visitors, was called off before 08:00.
Dundee United's game at Firhill followed three hours later.
But the Championship game between Dumbarton and Livingston and the League Two fixtures between East Fife and Clyde and East Stirlingshire against Arbroath go ahead following successful inspections.
Caley Thistle, whose game was first to be postponed, stated that the prospect of further poor weather also contributed to the decision.
Queen of the South were due to be visitors at Raith Rovers' Stark's Park in the Championship.
Forfar Athletic were the visitors at Cowdenbeath in League One, with Ayr United v Stenhousemuir also off in that division.
Queen's Park were travelling to Berwick, while Montrose were Stirling Albion's visitors.
Scottish Professional Football League, Saturday 30 January
Inverness CT P-P Hearts
Partick Thistle P-P Dundee United
Raith Rovers P-P Queen of the South
Ayr United P-P Stenhousemuir
Cowdenbeath P-P Forfar Athletic
Berwick Rangers P-P Queen's Park
Stirling Albion P-P Montrose