Does evolution select against genetic diversity?
TL;DR

In a population, directional selection reduces genetic diversity.

Simple scenario

In a population, directional selection reduces genetic variance (at the loci that are under selection and other linked loci). Selection selects for variants that are associated with the highest fitness. Hence, selection reduces the number of variants (or at least the frequency of the variants that are associated with a lower fitness).

Note that, by reducing genetic variance, selection also reduces heritability (see this post for definition) for the selected trait.

Note that, for a correct terminology, you should not say that selection "selects for" low genetic diversity. Selection "selects for" variants associated with high fitness which causes a reduction in genetic diversity. Selection indeed does not "select for" any population-wide statistic but only for specific variants in the population which affect those population-wide statistics.

Selection vs evolution

You say


  Does evolution select against genetic diversity?


Please do not confound "evolution" with "selection". There are a number of "drivers" of evolution other than selection (e.g. genetic drift, mutation, migration). Both selection and drift reduce genetic diversity, however, mutation and incoming migration will typically increase it.

Balancing selection

Note also that there are types of selection that maintain genetic variance such as negative frequency-dependent selection, or heterozygous advantage for examples. Those types of selection that maintain genetic diversity are called balancing selection.

Multiple populations

Imagine a scenario where two populations are present in two different environments. If there is directional selection going into opposite direction in each environment (aka local selection), then selection will still reduce within-population genetic diversity but will increase the among-population genetic diversity.

Definitions of genetic diversity

Genetic diversity is a concept used in population and evolutionary genetics. The term genetic diversity is typically defined as the probability of non-identity by state of two alleles. In a single population, this is identical as the definition of expected heterozygosity. Let $p$ be the allele frequency in a population, the genetic diversity $\pi$ at this locus in this population is defined as $\pi = 2p(1-p)$. 

More info about these definitions and their relationship to $F_{ST}$ (a widely used statistics of population divergence) in Nei (1973) and Charlesworth (1998).

Definitions of genetic variance

Genetic variance is typically a term used in quantitative genetics. One could say that genetic variance is defined by the phenotypic consequences of genetic diversity. See this post for the definition

For simplicity, above, I used the terms genetic diversity and genetic variance correctly but without highlighting that they take different definitions.

Intro to evolutionary genetics

Your question is a very introductory question in evolutionary genetics. You might be interested in some intro books (have a look at the post Books on population or evolutionary genetics).