  We derive analytical formulae for the Minkowski Functions of the cosmic
microwave background (CMB) and large-scale structure (LSS) from primordial
non-Gaussianity. These formulae enable us to estimate a non-linear coupling
parameter, f_NL, directly from the CMB and LSS data without relying on
numerical simulations of non-Gaussian primordial fluctuations. One can use
these formulae to estimate statistical errors on f_NL from Gaussian
realizations, which are much faster to generate than non-Gaussian ones, fully
taking into account the cosmic/sampling variance, beam smearing, survey mask,
etc. We show that the CMB data from the Wilkinson Microwave Anisotropy Probe
should be sensitive to |f_NL|\simeq 40 at the 68% confidence level. The Planck
data should be sensitive to |f_NL|\simeq 20. As for the LSS data, the late-time
non-Gaussianity arising from gravitational instability and galaxy biasing makes
it more challenging to detect primordial non-Gaussianity at low redshifts. The
late-time effects obscure the primordial signals at small spatial scales.
High-redshift galaxy surveys at z>2 covering \sim 10Gpc^3 volume would be
required for the LSS data to detect |f_NL|\simeq 100. Minkowski Functionals are
nicely complementary to the bispectrum because the Minkowski Functionals are
defined in real space and the bispectrum is defined in Fourier space. This
property makes the Minksowski Functionals a useful tool in the presence of
real-world issues such as anisotropic noise, foreground and survey masks. Our
formalism can be extended to scale-dependent f_NL easily.
