You do not mention whether your son is under age 19, or under age 24 and a full-time student. If he is, his income would not matter. From the phrasing of your question, I suspect he is not. So, he would no longer be a "qualifying child" for purposes of being your dependent. He could only continue to be your dependent under the "qualifying relative" rule.
Generally, you can claim your "qualifying relative" as a dependent if:
- The relative is a U.S. citizen, a U.S. national, a resident alien, or a resident of Canada or Mexico;
- The relative lived with you all year;
- The relative had gross income of less than $4,050.00 in 2016;
- You provide over half of their support; and
- No one else provided over half of the relative’s support.
As you can see, under this rule, your son's gross income would disqualify him from being your dependent.
For more information, please see Rules for Claiming a Dependent on Your Tax Return.