BERLIN—The Paris attacks have raised fears of terrorists slipping into Europe by posing as refugees. But in Germany, the top migrant destination, security officials have another worry: Local extremists will recruit the newcomers to join the Islamist cause once they arrive.

German authorities warn that migrants seeking out Arabic-language mosques in search of the familiar are increasingly ending up at those attended by Islamist radicals. In interviews, security officials from Berlin to the southwest German state of Saarland...