No, as subways in Tokyo are operated by private companies :
However, the Yamanote circular train line, which serves the 30 main touristic areas in Tokyo (Ueno, Akihabara, Shibuya, Harajuku, Shinjuku, Ikebukuro, etc.), is operated by Japan Railways and thus included in the JR Pass.
It is the same for numerous other lines that conveniently serve Tokyo’s agglomeration.
For first-time travelers in Japan, it is possible to travel several days in Tokyo using only the JR Pass most of the time.
Below is the JR transportation network map in Tokyo (click on the picture to enlarge):