Instabilities of a wake produced by a circular cylinder in a uniform water flow are studied experimentally when viscoelastic solutions are injected through holes pierced in the cylinder. It is shown that the viscoelastic solutions fill the shear regions and drastically modify the instabilities. The two-dimensional instability giving rise to the Kármán street is found to be inhibited: the roll-up process appears to be delayed and the wavelength of the street increases. The wavelength increase obeys an exponential law and depends on the elasticity number, which provides a ratio of elastic forces to inertial forces. The three-dimensional instability leading to the A mode is generally found to be suppressed. In the rare case where the A mode is observed, its wavelength is shown to be proportional to the wavelength of the Kármán street and the streamwise stretching appears to be inhibited. Injection of viscoelastic solutions also decreases the aspect ratio of the two-dimensional wake, and this is correlated with stabilization of the A mode and with changes in the shape of the Kármán vortices. The observations of this work are consistent with recent numerical simulations of viscoelastic mixing layers. The results suggest mechanisms through which polymers inhibit the formation of high-vorticity coherent structures and reduce drag in turbulent flows.