Will monosodium dihydrogen phosphate react as base or acid in water?
Monosodium dihydrogen phosphate, $\ce{H2PO4^-}$, is an amphoteric species and it will act as both an acid and a base. 
These are the related chemical equations:

\begin{align}
  \ce{H2PO4- + H2O &amp;&lt;=&gt; HPO4^2- + H3O+}  &amp; \mathrm{p}K_\mathrm{a} &amp;= 7.21\\
  \ce{H2PO4- + H2O &amp;&lt;=&gt; H3PO4 + OH-}     &amp; \mathrm{p}K_\mathrm{b} &amp;= 11.88
\end{align}

As an example, $\pu{0.1 M}$ solution of such a salt will have a pH of about $4.7$.
In other words, the acidic behaviour dominates over the alkaline one. This is due to the value of $\mathrm{p}K_\mathrm{a}=7.21$ (related to the acidic behaviour) compared to the $\mathrm{p}K_\mathrm{b}=11.88$ (related to the alkaline behaviour).