It marked the fifth straight match that Icardi, Serie A's joint top scorer last season with 29 goals, has missed in all competitions since being stripped of the club's captaincy as he demands a contract extension.
Luca Ceppitelli put Cagliari ahead after the half-hour mark by redirecting a free kick with a header. Eight minutes later, Lautaro Martinez equalized for Inter with a header from Radja Nainggolan's cross.
Leonardo Pavoletti then restored Cagliari's advantage with a low volley between two defenders. Cagliari had a chance to extend its lead but Nicolo Barella's penalty attempt sailed high over the bar in stoppage time.
Cagliari is 14th, nine points above the relegation zone. Milan hosts Sassuolo and Roma meets Lazio in the Rome derby.
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