Studies of solar-flare cosmic-ray particle transport in the interplanetary medium and data analysis of the fluctuating solar wind magnetic fields have revealed the existence of dominating, two-dimensional transverse magnetic fluctuations. Here it is demonstrated that the filamentation instability of counterstreaming magnetized plasmas provides a plausible mechanism for the origin of this two-dimensional turbulence component. Solar coronal mass ejections into the interplanetary medium, as well as overtaking solar wind streams in the appropriate center of plasma mass reference system, correspond to energetic collisions of plasma shells with different nonrelativistic velocities. By analyzing the dispersion relation, it is shown that these plasma shell collisions quickly lead to the onset of purely growing aperiodic plasma instabilities perpendicular to the flow direction if the flow velocity difference is larger than 1/2 times the local Alfven speed, where rn denotes the density contrast of the colliding shells. For typical coronal mass ejections and parameters that allow overtaking the solar wind stream, the instability condition is well fulfilled, and the calculated growth rates of the fluctuations are short compared to the dynamical flare timescales.