Reports first emerged on Tuesday that the former Aston Villa striker was being targetted by the Nerazzurri, before coach Andrea Stramaccioni later confirmed that the player would be given a trial before a decision was made on whether or not to sign him.
However, the 33-year-old has since failed to pass fitness tests and will therefore not be offered a contract with the club.
A statement on Inter's official website on Wednesday afternoon read: "Inter would like to thank Norwegian striker John Carew for the great dedication and professionalism he demonstrated.
"His current athletic condition, however, would require a medium to long period of specific individual work, which is not compatible with the needs of the club."
Inter has been desperately seeking cover for its forward positions ever since Diego Milito was ruled out for the season with a knee injury, and has also been linked with the likes of Angelos Charisteas and Ruud van Nistelrooy.
Carew has been without a club since he left West Ham United last summer.
The striker, who has 91 caps and 24 goals for Norway, has previously played for Aston Villa, Stoke City, Olympique Lyonnais, Valencia and Rosenborg.