This work proposes and investigates theoretically a biosensor that is an integrated plasmonic Mach-Zehnder interferometer. The biosensor consists of three sections. The first and third sections are input and output dielectric waveguides whose core is a silicon film. The second section is a combination of a surface plasmon polariton waveguide and a metal-insulator-silicon waveguide, which are separated by a thick gold film. The former and the latter function as sensing and reference arms, respectively. The latter supports a mode whose fields are highly enhanced in a thin insulator, silicon nitride film, and it has relatively small propagation loss. It is shown that the biosensor has insertion loss lower than 2 dB, and that it is very compact since the length of its second section for sensing is shorter than 6 μm. In addition, it is discussed that it can be easily implemented by using simple fabrication processes. Analyzed are the characteristics of sensing a refractive index change of liquid covering the biosensor. Despite its compactness, they are similar to those of previous surface plasmon interferometers. Also, its characteristics as a DNA sensor are analyzed. The analysis demonstrates that the biosensor can detect sensitively target single-stranded DNAs whose total weight is smaller than 10 fg.