Cannot use CDI constructor injection on EJBs

Issue

• We have an EJB where the constructor is annotated with @Inject. When we try to deploy it, we get this error:

ERROR [org.jboss.msc.service.fail] (MSC service thread 1-9) MSC00001: Failed to start service jboss.deployment.unit."test.war".INSTALL: org.jboss.msc.service.StartException in service jboss.deployment.unit."test.war".INSTALL: JBAS018733: Failed to process phase INSTALL of deployment "test.war"
        at org.jboss.as.server.deployment.DeploymentUnitPhaseService.start(DeploymentUnitPhaseService.java:123) [jboss-as-server-7.1.2.Final.jar:7.1.2.Final]
        at org.jboss.msc.service.ServiceControllerImpl$StartTask.startService(ServiceControllerImpl.java:1811) [jboss-msc-1.0.2.GA.jar:1.0.2.GA]
        at org.jboss.msc.service.ServiceControllerImpl$StartTask.run(ServiceControllerImpl.java:1746) [jboss-msc-1.0.2.GA.jar:1.0.2.GA]
        at java.util.concurrent.ThreadPoolExecutor$Worker.runTask(ThreadPoolExecutor.java:886) [classes.jar:1.6.0_35]
        at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:908) [classes.jar:1.6.0_35]
        at java.lang.Thread.run(Thread.java:680) [classes.jar:1.6.0_35]
Caused by: org.jboss.as.server.deployment.DeploymentUnitProcessingException: JBAS011030: Could not configure component TestBean
        at org.jboss.as.ee.component.deployers.EEModuleConfigurationProcessor.deploy(EEModuleConfigurationProcessor.java:91)
        at org.jboss.as.server.deployment.DeploymentUnitPhaseService.start(DeploymentUnitPhaseService.java:116) [jboss-as-server-7.1.2.Final.jar:7.1.2.Final]
        ... 5 more
Caused by: org.jboss.as.server.deployment.DeploymentUnitProcessingException: JBAS014227: EJB TestBean of type test.TestBean must have public default constructor
        at org.jboss.as.ejb3.component.EJBValidationConfigurator.configure(EJBValidationConfigurator.java:59)
        at org.jboss.as.ee.component.deployers.EEModuleConfigurationProcessor.deploy(EEModuleConfigurationProcessor.java:80)
        ... 6 more