Biologically induced changes in physical oceanic properties through phytoplankton provide potential positive and negative feedback loops. In particular, surface floating cyanobacteria, which are expected to be favored from future environmental conditions and can form large surface mats, can increase light absorption and the surface albedo and decrease momentum input from the atmosphere by wind. In this work we study the effect of a changing phytoplankton community composition to one dominated by buoyant cyanobacteria on the physical oceanic properties. We use the water column model General Ocean Turbulence Model and set up an idealized biological model taking into account the phytoplankton species' characteristics as well as the effects of biology on physics. The model results show that an increase of buoyant cyanobacteria leads to substantial changes in the seasonal cycle of the mixed layer. The results furthermore indicate that the effects due to altered absorption and biologically induced reduction of the wind drag are larger than contrary effects due to changes in the surface albedo. Overall, our model results suggest that the development of cyanobacterial surface blooms and their feedbacks on light absorption and wind drag need to be taken into account in ocean models used for climate scenarios in order to capture changes in the dynamics of the upper ocean.