Can we prohibit employees from working a second job?

Q. We have an employee who works a second job. He left work at lunch and went to a clinic because he didn't feel good. When he came back two-and-a-half hours later, he said he was leaving because the doctor told him to go home and sleep for a couple of days. I told him that if his second job interfered with his primary job, he may have to give the second job up. Was I wrong to tell him that? – Patsy, Texas