We present results from a new magnetohydrodynamic model of the inner heliosphere. We focus in this study on Carrington rotation 1892 which occurred during solar minimum, and simulate the solar wind and heliospheric magnetic field from 0.1 to 2 AU. We demonstrate the development of small scale (∼1° × 1° × 1 solar radius) structure, such as folds and ripples, on the surface of the heliospheric current sheet. In particular, we analyze the evolution of a current sheet fold forming by ∼1 AU, significantly narrowing by ∼1.5 AU (∼1° in width), and quickly disrupting afterwards. The disruption constitutes a process whereby the lower part of the current sheet fold separates from the main surface and, on a heliocentric spherical surface, appears as an island of outward polarity in the sea of the field of inward polarity. We show that this process is associated with non-radial motion of plasma and magnetic field induced inside a stream interaction region. In addition, we discuss evidence of magnetic reconnection in our simulation that involves flux tubes in the vicinity of the heliospheric current sheet. The simulations presented here provide a useful global 3-dimensional context for interpreting multiple current sheet crossings commonly observed by spacecraft as well as observations of magnetic reconnection in the solar wind.