  Spherically-symmetric ground states of alkali-metal atoms do not posses
electric quadrupole moments. However, the hyperfine interaction between nuclear
moments and atomic electrons distorts the spherical symmetry of electronic
clouds and leads to non-vanishing atomic quadrupole moments. We evaluate these
hyperfine-induced quadrupole moments using techniques of relativistic many-body
theory and compile results for Li, Na, K, Rb, and Cs atoms. For heavy atoms we
find that the hyperfine-induced quadrupole moments are strongly (two orders of
magnitude) enhanced by correlation effects. We further apply the results of the
calculation to microwave atomic clocks where the coupling of atomic quadrupole
moments to gradients of electric fields leads to clock frequency uncertainties.
We show that for $^{133}$Cs atomic clocks, the spatial gradients of electric
fields must be smaller than $30 \, \mathrm{V}/\mathrm{cm}^2$ to guarantee
fractional inaccuracies below $10^{-16}$.
