Transmembrane proteins frequently form (transient) oligomers on biomembranes, e.g., while participating in protein sorting and signaling events. Using coarse-grained membrane simulations we show here that transmembrane proteins show a subdiffusive motion on short time scales when being part of a linear oligomer, i.e., a flexible polymer, embedded in a two-dimensional membrane. Our results are in agreement with previous experimental observations. They further indicate that polymers of transmembrane proteins are well described by predictions from Rouse theory in two dimensions even in the presence of hydrodynamic interactions.