We report on a search for the charmless decays ${B}^{+}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{+}$ and ${B}^{0}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{0}$ that are strongly suppressed in the standard model. The analysis is based on a data sample of $657\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs collected at the $\ensuremath{\Upsilon}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider. We find no significant signal and set upper limits of $3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ for ${B}^{+}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{+}$ and $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ for ${B}^{0}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{0}$ at the 90% confidence level.