The 33-year-old - without a club since leaving West Ham in the summer - had been training with Inter with a view to joining until the end of the season.
But a short statement on the Serie A side's website said Carew's fitness was not at the required level.
It read: "FC Internazionale would like to thank Norwegian striker John Carew for the willingness and professionalism he has shown.
"His present physical condition, however, would require him to undergo a rather lengthy period of specific individual fitness work which is not compatible with the needs of the club."
Inter have been looking for attacking reinforcements since Diego Milito was ruled out for the season with damaged knee ligaments earlier this month.