Here's a study.

Schizophrenia occurs in national populations with an annual prevalence of 1.4 to 4.6 per 1000 and incidence rates of 16–42 per 100 000 (Jablensky, 2000). Although the incidence rates vary between countries by a factor of less than 3, wider ranges of variation are found among population subgroups within single countries. In the UK, for example, incidence rate ratios of 4 or above have been estimated both for the lowest social class in the indigenous White population and for Black immigrant groups. These data provide the most compelling evidence yet to hand for the role of socio-economic factors in aetiology.

I think the amount of additional schizophrenia is low enough that this isn't a major issue for immigration.