How does the naive Bayes classifier handle missing data in testing?
In evaluation (test) phase, when data point $x_n$ has $d$ missing features at indices $M=\{m_1,...,m_d\}$, corresponding terms $P(x_i|C_k),i \in M$ are simply removed from the classifier. That is, classifier
$$C(x_n) = \underset{k \in \{1,..,K\}}{\mbox{argmax }}P(C_k)\prod_{i}P(x_i=x_{n,i}|C_k)$$
is replaced with
$$C(x_n) = \underset{k \in \{1,..,K\}}{\mbox{argmax }}P(C_k)\prod_{\color{blue}{i:i \notin  M}}P(x_i=x_{n,i}|C_k)$$

where $i$ iterates over features, $x_{n,i}$ denotes the $i$-th feature of data point $n$, and there is $K$ classes in total.