  We investigate the impact of non-standard neutrino interactions (NSIs) on
atmospheric neutrinos using the proposed PINGU experiment. In particular, we
focus on the matter NSI parameters $\varepsilon_{\mu\tau}$ and
$|\varepsilon_{\tau\tau} - \varepsilon_{\mu\mu}|$ that have previously been
constrained by the Super-Kamiokande experiment. First, we present approximate
analytical formulas for the difference of the muon neutrino survival
probability with and without the above-mentioned NSI parameters. Second, we
calculate the atmospheric neutrino events at PINGU in the energy range (2-100)
GeV, which follow the trend outlined on probability level. Finally, we perform
a statistical analysis of PINGU. Using three years of data, we obtain bounds
from PINGU given by $-0.0043~(-0.0048) < \varepsilon_{\mu\tau} <
0.0047~(0.0046)$ and $-0.03~(-0.016) < \varepsilon_{\tau\tau} < 0.017~(0.032)$
at 90 % confidence level for normal (inverted) neutrino mass hierarchy, which
improve the Super-Kamiokande bounds by one order of magnitude. In addition, we
show the expected allowed contour region in the
$\varepsilon_{\mu\tau}$-$\varepsilon_{\tau\tau}$ plane if NSIs exist in Nature
and the result suggests that there is basically no correlation between
$\varepsilon_{\mu\tau}$ and $\varepsilon_{\tau\tau}$.
