Magnetohydrodynamics plays important role to manipulate the physiological fluids due to magnetic nature of physiological fluids. Magnetohydrodynamics pumps are a robust technology which provide more elegant and sustainable performance compared with conventional medical pumps. To study the effects of suspension of the nanoparticles (drugs) in physiological fluids (blood) flow are important in biomedical science and engineering. Motivated by such applications, an analytical approach is presented to study the nanoparticle shape effects on peristaltic transport of nanofluids in presence of magnetohydrodynamics in the present article. A two dimensional continuity, momentum and energy equations are considered to govern the present biophysical model. The governing equations are also linearized using lubrication theory where we consider the low Reynolds number and long wavelength approximations. Closed form solutions are obtained for axial velocity, axial pressure gradient, temperature, pressure rise, wall shear stress and stream function. The effects of three different type of shapes (bricks, cylinders, and platelets) of nanoparticles on peristaltic pumping characteristics and thermal characteristics are computed with the help of graphical illustrations. The interesting outcomes of this study are relevant to more realistic designs for ocular peristaltic pumps in drug delivery systems.