Oceanic mesoscale eddies (with a diameter of 50-100 km) are known to be associated with significant vertical tracer fluxes in the upper few hundred meters. In particular, they are important for the biogeochemical system, accounting for 20-30% of the vertical nutrient transport. However, estimates of the global tracer fluxes neglect the role played by thin elongated filaments (with a width of 5-10 km). These sub-mesoscale structures are produced by eddy interactions and ubiquitous in regions between eddies. We use a Surface Quasi-Geostrophic model to quantify their impact on the net vertical tracer flux into the surface layers. We show that eddy interactions are an important source of tracer injection because they lead to the production of filaments and to large vertical velocities within these structures. This is attributed to the frontogenetic dynamics induced by the horizontal stirring processes. When taking into account this process for the global statistics of tracer injection, the tracer flux associated with the filaments is as significant as that associated with the eddies. This outcome points out the necessity to explicitly include the filamentation process in global ocean model studies.