  We show that the carrier-mediated exchange interaction, the so-called RKKY
coupling, between two magnetic impurity moments in graphene is significantly
modified in the presence of electron-electron interactions. Using the
mean-field approximation of the Hubbard-$U$ model we show that the
$(1+\cos(2{\bf k}_D\cdot {\bf R})$-oscillations present in the bulk for
non-interacting electrons disappear and the power-law decay becomes more long
ranged with increasing electron interactions. In zigzag graphene nanoribbons
the effects are even larger with any finite $U$ rendering the long-distance
RKKY coupling distance independent. Comparing our mean-field results with
first-principles results we also extract a surprisingly large value of $U$
indicating that graphene is very close to an antiferromagnetic instability.
