"Could not initialize JBossNativeJdbcExtractor" on EAP 6

Issue

When deploying our Spring-based application on EAP 6, we get th efollowing error:

ERROR [org.apache.catalina.core.ContainerBase.[jboss.web].[default-host].[/myapp]] (ServerService Thread Pool -- 1) JBWEB000289: Servlet api-spring-mvc threw load() exception: java.lang.IllegalStateException: Could not initialize JBossNativeJdbcExtractor: neither JBoss 7's [org.jboss.jca.adapters.jdbc..WrappedConnection] nor traditional JBoss [org.jboss.resource.adapter.jdbc..WrappedConnection] found
    at org.springframework.jdbc.support.nativejdbc.JBossNativeJdbcExtractor.<init>(JBossNativeJdbcExtractor.java:88) [spring-jdbc-3.2.2.RELEASE.jar:3.2.2.RELEASE]
    at sun.reflect.GeneratedConstructorAccessor50.newInstance(Unknown Source) [:1.6.0_65]
    at sun.reflect.DelegatingConstructorAccessorImpl.newInstance(DelegatingConstructorAccessorImpl.java:27) [classes.jar:1.6.0_65]
    at java.lang.reflect.Constructor.newInstance(Constructor.java:513) [classes.jar:1.6.0_65]
    at org.springframework.beans.BeanUtils.instantiateClass(BeanUtils.java:148) [spring-beans-3.2.2.RELEASE.jar:3.2.2.RELEASE]